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1
Put oven racks in upper and lower thirds of oven and preheat oven to 350F.
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2
Beat together butter, sugar, vanilla, and salt in a bowl with an electric mixer at medium-high speed until light and fluffy, about 3 minutes.
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3
Reduce speed to low, then add flour and poppy seeds and mix until just combined.
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4
Transfer dough to plastic bag and pat out dough to size of bag.
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5
Press out excess air and seal bag.
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6
Roll out dough with a rolling pin to flatten evenly and to fill bag (dough will be about 1/4 inch thick).
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7
Freeze dough on a baking sheet until firm, at least 20 minutes.
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8
Open bag and cut apart along seams, reserving bag for rolling scraps.
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9
Cut out as many ovals as possible with cookie cutter, reserving scraps, and transfer to 2 ungreased large baking sheets, arranging about 1/2 inch apart.
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10
Bake cookies, switching position of sheets halfway through baking, until edges are golden, 16 to 20 minutes total.
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11
Cool cookies on sheets on racks 5 minutes, then transfer with a spatula to racks to cool completely.
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12
Gather and reroll scraps using reserved plastic bag (to keep dough from sticking), then cut out and bake more cookies in same manner.
