Salt-As-You-Go Pasta

Bring 6 quarts water to a boil in a large pot; season with salt. The water should taste like ocean water, so keep adding salt until it tastes very, very saline (you should use around 1/4 cup). Meanwhile, heat 1/4 cup oil in a large skillet over medium. Add shallots, garlic, and 1/2 tsp. red pepper flakes; season lightly with salt. Cook, stirring occasionally, until shallots are translucent, about 4 minutes. Remove from heat and set aside. Remove florets from broccolini and cut into bite-size pieces. Slice stems into 1/2" pieces. Add to boiling water. Cook 1 minute, then, using a spider or slotted spoon, transfer to reserved skillet. Return water in pot to a boil and cook tubetti, stirring occasionally, until very al dente, 7 –9 minutes. Drain, reserving 3/4 cup pasta cooking liquid. Add pasta and pasta cooking liquid to skillet, tossing to combine. Cook over medium-high heat, gradually adding 1 1/2 oz. Parmesan and tossing often, until pasta is al dente and liquid has reduced to form a thick, glossy sauce, about 4 minutes. Taste and season with more salt if needed. To serve, squeeze lemon wedges over pasta, drizzle with oil, and top with more grated Parmesan and red pepper flakes.