1. In the bowl of an electric mixer fitted with the whisk attachment, combine yeast, 1 1/2 teaspoons flour, and sugar. Stir in 1/4 cup of the warm water, and let stand until foamy, about 10 minutes.

2. Whisk together the remaining 3 cups flour, cornmeal, rosemary, 1 teaspoon salt, and 1 1/2 teaspoons pepper; add to the yeast mixture. Using the dough hook, mix on low speed while slowly adding the remaining 1 cup of warm water. Mix, adding more warm water, if necessary, 1 tablespoon at a time, until the dough starts to pull away from the sides of the bowl. Mix until the dough is smooth and elastic, 5 to 6 minutes. Turn out the dough onto a clean surface, and knead four turns into a ball.

3. Place the dough in a lightly oiled large bowl, and coat the dough with the oil. Cover tightly with plastic wrap, and let the dough rise in a warm place until doubled in size, about 1 hour. Turn out onto a clean surface; divide into 6 smaller balls, each about 4 inches in diameter. Transfer the balls to a parchment-lined baking sheet, and loosely cover them with plastic wrap.

4. Preheat the oven to 400 degrees. On a lightly floured surface, shape one of the balls into a 3-by-5-inch rectangle, then roll it out to a 5-by-17-inch rectangle; it should be very thin. Place on the diagonal on an ungreased baking sheet. Slice the onion lengthwise as thinly as possible, leaving the root end intact. Fan out each slice of onion. Brush the surface of the dough with olive oil; place 3 or 4 sage leaves, 2 to 3 slices of onion, 2 to 3 slices of tomatillo, and 2 to 4 slices of tomato on top. Sprinkle with salt and pepper. Brush again lightly with olive oil. Repeat with remaining dough, and place on the sheet.

5. Bake until the flatbread turns golden brown, 12 to 14 minutes. Transfer the flatbread to a wire rack to cool. Working in batches, roll out, top, and bake remaining dough. Store in an airtight container up to 1 week.