Trim and discard the bottom 1/2-inch from the broccolini. Then cut the broccolini into 1-inch pieces. Steam broccolini covered in small skillet in 1/2 inch boiling water for 3 minutes, cold shock, and drain. Combine broccolini and pasta in a bowl.
Return pan to stove over low heat and saute shallots and garlic in oil 2 minutes. Pour warm oil over pasta and broccolini. Crumble ricotta salata over pasta. Sprinkle the pasta with thyme, salt, and pepper, and toss to combine. Adjust seasonings and garnish salad with halved grape tomatoes.