For the dough: Combine the 1 3/4 cups flour with the baking soda and salt in a large bowl. Whisk to eliminate any lumps. Pour in the milk and 1/4 cup of the olive oil and mix until a dough forms. Grease another large bowl with the remaining 1 tablespoon oil. Add the dough, cover with a kitchen towel or plastic wrap, and set aside for 10 minutes.
Meanwhile, make the filling: Heat a large skillet over medium-high heat. Add 2 tablespoons of the oil. Add the sausage and cook, breaking it up with a wooden spoon, until browned, about 5 minutes. Move the sausage to one side of the skillet, add the onions and season them with salt and pepper. Cook, stirring occasionally, until softened, about 3 minutes. Remove from the heat and set aside.
In another large skillet, heat the remaining 2 tablespoons olive oil over high heat. Add the garlic, broccoli rabe and red pepper flakes. Season with salt and pepper. Cook, stirring occasionally, until the rabe turns bright green, 3 to 4 minutes. Remove from the heat and sprinkle with the lemon juice. Set aside.
Heat a griddle over medium-high heat. Portion the dough into 6 balls. On a lightly floured surface, roll the balls until about 1/4 inch thick. Place 2 rounds onto the hot griddle. Cook until browned on one side and bubbles begin to form, about 1 minute. Flip and cook the other side for 30 seconds. Transfer the flatbread to a baking sheet. Keep the griddle over the heat.
Place some of the sausage filling and broccoli rabe on one half of each flatbread. Top each with the grated cheese (or 2 slices of cheese) and fold into a half moon. Place the sandwiches back on the griddle and weigh them down with a foil-covered brick or small cast-iron skillet. Cook until the cheese melts, about 1 minute. Repeat with the remaining dough and sandwiches. Remove from the heat, slice in half and serve.