Cook pasta according to package directions. Meanwhile, heat 3 tbsp. oil over medium heat in a large frying pan. Add Romanesco and 1/2 tsp. salt and cook, stirring occasionally, until tender-crisp, about 5 minutes. Add 1 tbsp. more oil to pan along with garlic and chile flakes. Cook until garlic is fragrant and light golden and Romanesco is tender, about 5 minutes more.
Drain pasta, reserving 1 cup pasta water, and return to pot. Stir in Romanesco mixture, lemon zest, almonds, cheese, remaining 3 tbsp. oil and 1/4 tsp. salt, and enough pasta water to moisten (about 3/4 cup).