Preheat the oven to 350°F. Place a rimmed baking sheet on the oven rack or set one aside for assembly.
Prepare the beans: if using canned pinto beans, drain and rinse them, then puree with the listed 1/4 cup water in a blender until smooth; if using canned refried beans, use them as is. Measure out 1 cup total.
Cook the meat: heat a large skillet over medium. Add 1/2 pound lean ground turkey or lean ground beef and cook, breaking it up with a spatula, until no pink remains, about 8–10 minutes. During cooking, add 1/2 tablespoon chili powder, 1 teaspoon cumin, and 1/4 teaspoon salt and stir to combine. Drain excess fat if desired and remove from heat.
Divide the prepared ingredients into three portions: split the cooked meat into three equal portions, measure three 1/3-cup portions of the beans (total 1 cup), and divide the 1 cup shredded cheese into three equal portions (about 1/3 cup each).
Assemble on the baking sheet: place one tortilla on the sheet. Spread one 1/3-cup portion of beans evenly over the tortilla, sprinkle one portion of cheese, and distribute one portion of meat on top. Place a second tortilla over this and repeat (beans, cheese, meat). Place the third tortilla on top and add the final beans, cheese, and meat.
Bake in the preheated oven about 10 minutes, until the cheese is melted and the tortilla edges are golden.
Remove from the oven and top with the 1 cup ribbon-sliced romaine lettuce and the diced medium tomato.
Cut the assembled Southwestern pizza into 4 slices and serve.