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1
Stir yeast and sugar into warm water in measuring cup and let stand until foamy, about 5 minutes.
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2
(If mixture doesn't foam, discard and start over with new yeast.)
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3
Stir together 1 1/4 cups flour, thyme, salt, and cayenne, then make a well in center and add yeast mixture and oil, stirring to form a dough.
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4
Turn out dough onto a lightly floured surface and knead in 2 to 3 tablespoons flour (dough should be moist but not sticky).
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5
Knead until smooth and elastic, about 6 minutes, then transfer to a lightly oiled large bowl and let rise, covered with plastic wrap, in a draft-free place at warm room temperature until doubled in bulk, 1 1/2 to 2 hours.
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6
Preheat oven to 450F.
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7
Roll out dough as thin as possible (into an 18-inch square) with a lightly floured rolling pin on a lightly floured surface.
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8
Sprinkle with kosher salt and gently press salt to help adhere.
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9
Cut dough into 1-inch squares with a pizza wheel or large sharp knife.
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10
Transfer with a lightly floured metal spatula to 3 lightly oiled baking sheets, placing squares close together.
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11
Bake in batches in middle of oven, rotating sheets halfway through baking, until bottoms are golden (tops will remain pale), 6 to 7 minutes.
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12
Transfer to a rack to cool completely.
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13
(Crackers will crisp as they cool.)
