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Preheat the oven to 375F.
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Combine the flour, cornstarch, sugar, and salt in a food processor and pulse once or twice.
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(Its important to process the ingredients gently, letting the machine run no longer than necessary at each stage so as not to toughen the batter.)
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Add the butter and pulse 10 or 20 times, until the butter and flour are well combined.
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Add the vanilla and the egg and pulse 3 or 4 times.
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Add about half the milk and pulse 2 or 3 times.
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Add the remaining milk a little at a time, pulsing once or twice after each addition, until the dough holds together in a sticky mass.
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(You can, of course, also make this batter in a standing mixer or by hand.
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In either case, cream together the butter and sugar first, then add the mixed dry ingredients.)
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Drop rounded teaspoons of dough (you can make the cookies larger or smaller if you like) onto a nonstick baking sheet, a sheet lined with parchment paper, or a lightly buttered baking sheet.
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If you want flat cookies, press the balls down a bit with your fingers or the back of a spatula or wooden spoon.
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Bake for 10 to 12 minutes, checking every minute or so after 8 minutes since most oven temperatures are slightly inaccurate, or until the cookies are done as you like them.
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Cool on a rack, then serve or store in a covered container for up to 3 days.
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Bake at 350F for a minute or two longer.
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The cookies wont brown on the edges as they will at 375F, but they will be crisp.
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Or bake for an extra minute or two at 375F for browned and crisp cookies.
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Butterscotch Cookies: Substitute half or more brown sugar for the white sugar or simply add 1 tablespoon molasses along with the egg.
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Citrus Cookies: Do not use the vanilla; add 1 tablespoon fresh lemon juice and 2 teaspoons grated lemon zest along with the egg.
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The same can be done with orange juice and zest.
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A couple tablespoons of poppy seeds go well here also.
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Chocolate Chip Cookies: Stir about 1 cup chocolate chips into the finished batter.
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(The butterscotch batter variation is good here.)
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Spice Cookies: Add 1 teaspoon ground cinnamon, 1/4 teaspoon each ground allspice and ground ginger, and 1 pinch ground cloves and mace or nutmeg to the dry ingredients.
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Ginger Cookies: Add 1 tablespoon ground ginger to the dry ingredients.
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For even better flavor, add 1/4 cup minced crystallized ginger to the batter by hand (this works well in addition to or in place of the ground ginger).
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Chunky Cookies: To the finished batter, add about 1 cup M&Ms (or other similar candy) or roughly chopped walnuts, pecans, or cashews; slivered almonds; raisins; coconut; dried cherries; and so on.
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Or combine any chunky ingredients you like.
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Rolled Cookies: Freeze the dough for 15 minutes or refrigerate it for about 1 hour (or longer).
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Work half the batter at a time and roll it on a lightly floured surface; it will absorb some flour at first but will soon become less sticky.
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Do not add more flour than necessary.
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Roll about 1/4 inch thick and cut with any cookie cutter; decorate as you like.
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Bake as directed, reducing the cooking time to 8 to 10 minutes.
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Puffy Cookies: The basic cookies are flat.
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For airier cookies, add 1/2 teaspoon baking powder to the dry ingredients.
