Step 1
Heat 2 Tbsp. extra-virgin olive oil in a medium Dutch oven or other heavy pot over medium-high. Arrange about 1″ pieces of 1 lb. hot or sweet Italian sausage, casings removed, in pot in a single layer. Cook, undisturbed, 3 minutes, then continue to cook, stirring occasionally with a wooden spoon or heatproof rubber spatula, until browned all over and just cooked through, 3–4 minutes more. Using a slotted spoon, transfer sausage to a plate.
Step 2
Place 1 medium onion, chopped, in same pot and season with kosher salt. Cook, stirring often, until slightly softened and starting to brown, about 3 minutes. Add 5 garlic cloves, thinly sliced, and one 4.5-oz. tube double-concentrated tomato paste (about ½ cup) and cook, stirring often, until paste is starting to stick to pot and has darkened significantly, about 3 minutes. Pour in 2 cups water, scraping up any browned bits stuck to bottom of pot.
Step 3
Pour in 4 cups low-sodium chicken broth and add 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt. Increase heat to high and bring to a boil. Add 10 oz. dried lasagna noodles (about 10 noodles), broken into 2″–3″ pieces, and cook, stirring often, until very al dente, about 9 minutes.
Step 4
Meanwhile, place 1 cup whole-milk fresh ricotta in a small bowl and season with salt and freshly ground pepper; mix well.
Step 5
Stir another 2 cups water into soup (it will have thickened up by this point); return sausage to pot. Reduce heat to low and cook just until meat is warmed through, about 5 minutes. Remove pot from heat and stir in 5 oz. fresh baby spinach; season soup with more salt and pepper if needed.
Step 6
Ladle soup into bowls. Top each with a dollop of ricotta mixture and season with more pepper.
