In a large bowl, dissolve yeast in 1 cup warm water (about 100°). Let sit until foamy, about 5 minutes. Stir in flours, 2 tbsp. oil, and 1 tsp. salt. (Dough will be stiff.) Cover bowl with plastic wrap and let sit in a warm place to rise until 1 1/2 times its original volume, about 1 hour.
Meanwhile, halve onion lengthwise, peel, and thinly slice. In a bowl, combine onion and rosemary with remaining 2 tbsp. oil, the vinegar, remaining 1 tsp. salt, and the chile flakes. Cover; set aside.
Preheat oven to 450°. Lightly sprinkle 2 baking sheets with semolina and set aside. Turn risen dough out onto a floured surface. Knead dough just until it feels smooth, about 10 times. Divide into 32 balls. Set 16 balls aside and cover with plastic wrap; roll the others as thinly as possible. Put 8 rounds on each baking sheet. Top each with a scant 1 tbsp. onion mixture and 1 1/2 tsp. blue cheese. Bake until browned and sizzling, about 15 minutes. Repeat with remaining dough balls, onion mixture, and cheese. Serve hot or warm.
Wine pairing: Chateau Ste. Michelle Cold Creek Vineyard Riesling 2006 (Columbia Valley; $14)
Note: Nutritional analysis is per flatbread.