On a clean work surface or in a large bowl, pile 2 cups of all-purpose flour, make a well in the center, sprinkle ½ teaspoon salt around the edges, pour in about ½ cup warm water, and use a fork to gradually incorporate the flour until a shaggy dough forms. Add remaining warm water a little at a time, kneading until the dough is firm but pliable and not sticky.
Knead the dough vigorously for 8–10 minutes until smooth and elastic; form into a ball, cover with plastic wrap or a damp towel, and let rest at room temperature for at least 30 minutes.
Unwrap the rested dough, keep half covered, and on a lightly floured surface roll out into a sheet about 1/8-inch thick. Cut into strips roughly ½-inch wide and 2–3 inches long. Roll each strip under your palms on the work surface, applying gentle pressure from center outward to form a twisted rope shape, and place on a floured baking sheet.
Bring a large pot of generously salted water to a rolling boil, add the strozzapreti, stir gently to prevent sticking, and cook 5–7 minutes or until al dente.
Drain the pasta, reserving ½ cup of pasta cooking water, then toss the strozzapreti immediately with your favorite sauce (adding pasta water as needed) and serve.