Stark korvragù med saxklippta nudlar

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1. 1
   Mix 2 cups (250 g) all-purpose flour, 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt, and ½ cup plus 1 Tbsp. water in a large bowl with your hands until a shaggy dough comes together. Knead in bowl, incorporating any loose bits, until dough forms into a smooth ball and no longer sticks to bowl, about 2 minutes. If dough is not coming together, mix in more water ½ tsp. at a time; if dough is too sticky, mix in more flour 1 tsp. at a time. Cover bowl with a damp paper towel or plastic wrap and let dough rest at room temperature while you prepare the ragù. Do ahead: Dough can be made 1 day ahead; wrap tightly and chill. Bring to room temperature before using.
2. 2
   Heat 2 Tbsp. extra-virgin olive oil in large Dutch oven or other heavy pot over medium-high. Cook 1 lb. spicy Italian sausage, casings removed, breaking up with a wooden spoon, until browned and cooked through, 6–10 minutes. Using a slotted spoon, transfer sausage to a plate, leaving fat behind.
3. 3
   Add 3 large shallots, halved, thinly sliced, 6 garlic cloves, coarsely chopped, ¼ cup gochujang, and 1 Tbsp. Diamond Crystal or 1¾ tsp. Morton kosher salt to pot. Cook, stirring often, until shallots are softened and gochujang is slightly darkened in color, 6–8 minutes. Stir in one 15-oz. can crushed tomatoes, 2 Tbsp. unsalted butter, cut into ½" pieces, 1 tsp. dried thyme, and 1 tsp. sugar. Return sausage along with any accumulated juices to pot. Reduce heat to low, cover, and simmer, stirring occasionally, until fat pools on surface of sauce, 30–40 minutes.
4. 4
   Bring a medium pot of water to a simmer. Coat a pair of kitchen shears with vegetable oil and snip off ½" pieces of dough directly into simmering water. When all of dough has been snipped, increase heat and bring water to a boil. Cook noodles, stirring occasionally to prevent sticking, until most have floated to the surface, about 3 minutes. Drain, reserving ½ cup noodle cooking liquid.
5. 5
   Stir noodles into ragù along with reserved noodle cooking liquid, 2 oz. Parmesan, finely grated, and remaining 2 Tbsp. unsalted butter, cut into ½" pieces. Increase heat to medium-high and cook, stirring vigorously, until butter is melted, cheese is combined, and sauce coats noodles, about 3 minutes. Remove from heat and stir in 2 Tbsp. red wine vinegar. Taste and add more salt if needed.
6. 6
   Divide noodles among shallow bowls; top with more Parmesan.