Umbrian Flat Bread Sandwiches (Torta al Testo)

In a small bowl, stir together yeast and 10 tbsp. water heated to 115°; let sit until foamy, about 10 minutes. Combine flour and salt in a food processor; pulse to blend. Add 1 tbsp. olive oil to yeast mixture and, with food processor running, pour in yeast mixture. Process until a dough forms. Transfer dough to a lightly floured surface; knead for 6 minutes. Form dough into a ball; transfer to a large oiled bowl. Cover bowl with plastic wrap; let dough rise until doubled in size, about 1 1⁄2 hours.

Punch the dough down; divide in half. Lightly flour one piece of dough and, using a rolling pin, roll into a 9" disk. Place disk on a floured baking sheet. Repeat with remaining dough. Cover dough with a damp towel; let sit for 15 minutes. Heat a 12" cast-iron skillet over medium heat. Working in 2 batches, cook each dough disk, flipping occasionally, until light brown, about 10 minutes.

Heat 3 tbsp. olive oil in a 12" skillet over medium-high heat. Add garlic and chile flakes; cook, stirring, until golden brown, about 3 minutes. Add broccoli rabe and cook until hot, about 3 minutes; transfer to plate. Return skillet to medium-high heat and add remaining oil. Add sausages; cook, turning, until browned, about 5 minutes. Halve sausages lengthwise.

Slice each flat bread in half horizontally to create two rounds; arrange broccoli rabe and sausages on bottom half of bread, drizzle with a little oil, and top with other half. Cut sandwiches into 8 wedges and serve.