1. Brush a large bowl with oil; set aside. Stir yeast, 1 1/2 teaspoons flour, and the sugar in the bowl of an electric mixer. Stir in 1/4 cup warm water, and let stand until creamy, about 10 minutes.

2. Whisk remaining 3 cups flour, the cornmeal, rosemary, 1 teaspoon salt, and 1 1/2 teaspoons pepper in a medium bowl; add to yeast mixture. Attach to mixer fitted with the dough hook. With mixer on low speed, gradually add remaining cup warm water; mix until dough just comes together, adding more warm water, 1 tablespoon at a time, if needed. Continue to mix until dough is smooth and elastic, 5 to 6 minutes more. Turn out onto a work surface; knead 4 times into a ball.

3. Transfer dough to oiled bowl; cover with plastic wrap. Let rise in a warm, draft-free place until doubled in bulk, about 1 hour. Turn out onto a work surface; evenly divide into 12 balls. Transfer to a baking sheet lined with parchment paper; loosely cover with plastic wrap.

4. Preheat oven to 400 degrees. Working with 1 ball of dough at a time, roll out on a lightly floured surface to a 4-by-11-inch oval. Brush with oil. Repeat with remaining balls of dough. Fan out each slice of onion. Divide sage leaves and slices of onion, tomatillo, and tomato among flatbreads; season with salt and pepper.

5. Transfer 2 flatbreads to a baking sheet. Bake until flatbreads turn golden brown, 12 to 14 minutes. Transfer to a wire rack to cool completely. Repeat with remaining flatbreads.