- 2 cups warm water (about 110°)
- 1 packet (1 1/4 ounces) active dry yeast
- 1 Tbsp. sugar
- 5 cups bread (or all-purpose) flour
- 1/2 cup fine- or medium-ground cornmeal , plus 4 tsp. for pizza peel
- 3 Tbsp. extra-virgin olive oil
- 1 1/2 Tbsp. kosher salt
- 1/4 cup extra-virgin olive oil , divided, plus more for drizzling
- 1/2 cup raw almonds , coarsely chopped
- 1 clove garlic , minced
- 3/4 tsp. smoked paprika
- Red pepper flakes , to taste
- 2 yellow peaches , cut into 1/2-inch-thick slices
- 1/3 pound Serrano ham , thinly sliced
- 1/2 pound soft ripened sheep's-milk cheese or goat's-milk cheese , such as Nevat, thinly sliced
- 1 cup baby arugula or mizuna
- 3/4 cup fresh oregano
- Kosher salt , to taste
To make dough: In the bowl of a stand mixer fitted with a dough hook, combine warm water, yeast, and sugar; let sit until foamy, about 5 minutes. Add flour, cornmeal, olive oil, and salt; mix until combined, about 5 minutes. Cover with a damp towel and let sit 20 minutes. Mix on medium speed until dough is smooth, about 5 minutes more. Cover and refrigerate 6 hours or overnight. (Take dough out of refrigerator 1 hour before starting to make the flatbreads.)
To make almond topping: In a medium skillet, heat 3 tablespoons olive oil over medium-high heat. Add almonds, minced garlic, and paprika; cook, stirring, until almonds are golden, about 3 minutes; transfer to a small bowl and set aside.
To make flatbreads: Put a pizza stone or heavy pieces of foil on a cold grill. Heat grill at medium-high heat (450°) for 10 minutes. Divide dough into 4 pieces. Dust a pizza peel or the back side of a sheet tray with 1 teaspoon cornmeal. Working with 1 piece at a time, stretch dough on a lightly floured surface until 1/4-inch thick and about 12" x 14", and transfer to prepared pizza peel. Top dough piece with 1 teaspoon olive oil, red pepper flakes to taste, a few slices of garlic, and a few slices each of peaches, ham, and cheese. Carefully slide flatbread onto pizza stone and immediately lower heat on grill to low. Cover grill and cook until bottom of crust is golden brown and crisp, cheese is melted, and peaches are soft, 6 to 8 minutes. Repeat with 3 remaining pieces of dough.
Remove flatbreads from grill and top each with a small handful of greens, 3 tablespoons oregano, and 2 tablespoons almond topping. Season to taste with salt and a drizzle of olive oil. Serve immediately.