In a large bowl, sprinkle yeast over 1 1/2 cups warm (110°) water. Let stand until yeast is softened, about 5 minutes. Stir in 1 teaspoon salt and 1 tablespoon olive oil. Gradually stir or, with an electric mixer on low speed, beat in 3 1/2 cups flour until mixture forms a soft dough.
If using a dough hook, beat on high speed until dough no longer feels sticky and pulls cleanly from bowl, 5 to 7 minutes. If dough is still sticky, beat in more flour, 1 tablespoon at a time. If kneading by hand, scrape dough onto a lightly floured board. Knead until smooth, springy, and no longer sticky, 15 to 20 minutes; add flour as required to prevent sticking. Place dough in an oiled bowl; turn dough over to coat top. Cover dough with plastic wrap and let rise in a warm place until doubled, 35 to 45 minutes. Punch dough down, cover, and chill up to 8 hours (see notes).
Meanwhile, in a 10- to 12-inch frying pan over medium-high heat, stir bacon until browned and crisp, about 5 minutes. Transfer to paper towels to drain. Reserve 1 tablespoon bacon drippings to dress greens, if desired.
At least 2 hours before serving, remove dough from refrigerator and let stand at room temperature for 45 minutes (see notes). Scrape onto a lightly floured board and press gently to expel air. Divide dough into four pieces. Cover with plastic wrap and let rest 10 minutes. Roll or gently stretch one piece at a time into a 13- by 7-inch oval about 1/16 inch thick. Place each on an oiled and cornmeal-dusted 12- by 15-inch rimless baking sheet; if necessary, stretch dough to reshape.
Brush each oval with about 1/2 tablespoon olive oil and sprinkle with about 1/3 cup cheese. Arrange a quarter of the cooked bacon evenly over each.
Bake flatbreads two at a time in a 450° oven for 10 minutes. Remove from oven and crack 3 eggs onto each oval (for firm-cooked eggs, crack eggs onto flatbread 5 minutes into baking). Sprinkle lightly with salt and pepper.
Return flatbreads to oven, switching pan positions, and bake until crust is well browned, 5 to 8 minutes longer.
Meanwhile, in a large bowl, mix 1 tablespoon olive oil or reserved bacon drippings and the vinegar. Add spinach and frisée and mix to coat.
Slide each flatbread onto a cutting board or plate. Mound dressed greens equally on top. Cut each oval in half lengthwise, then crosswise into eight slices. Add salt and pepper to taste.