Place a large pot of water over high heat and bring up to a boil to cook the pasta. Once boiling, add some salt and cook the pasta until al dente according to package directions.
While the water for the pasta is coming up to a boil, start the broccolini: Place a large skillet with high sides with 1 to 2 inches of water over high heat and bring up to a boil. Add some salt and broccolini, using a spoon or tongs settle the broccolini into the water. Cover and cook for 2 minutes, drain and reserve.
Return the skillet to the stovetop and place over medium-high heat with 2 turns of the pan of EVOO, about 2 tablespoons. Once the oil is hot, add onion and garlic, and season with some salt and pepper. Cook, stirring frequently, for 3-4 minutes. Add the broccolini to the pan and continue to cook for 1-2 minutes.
While the pasta is cooking, combine the ricotta and Parmigiano with a ladleful of the pasta cooking liquid, salt and pepper in a serving dish. Stir to combine.
When the pasta is cooked, drain it and add half the pasta to the skillet with the broccolini, reserve the second half for Pasta and Eggs for Breakfast the next morning.
Add broccolini and pasta to the serving bowl and toss with the ricotta/Parmigiano mixture. Season to taste. Top with the grape tomatoes and serve.