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Bring medium pot salted water to boil
In large pan, heat 2 teaspoons olive oil over medium-high until hot. Add broccoli florets and season with sea salt and pepper. Cook 3 to 4 minutes, stirring occasionally, or until lightly browned and slightly softened.
Add shallot, garlic, and half of butter to pan. Cook 2 to 3 minutes, stirring frequently, or until softened. Add ¼ cup water; season with sea salt and pepper. Cook 2 to 3 minutes, stirring occasionally, or until broccoli has softened and water has cooked off.
Add pasta to boiling water and cook until al dente. Reserve ½ cup pasta cooking water; drain thoroughly.
Add cooked pasta, remaining butter, half of reserved pasta cooking water and pinch of chili flakes to pan with broccoli. Continue to cook, stirring vigorously, 30 seconds to 1 minute, or until pasta is thoroughly coated. (If pasta seems dry, gradually add remaining cooking water to achieve your desired consistency.) Turn off heat and stir in crème fraîche. Season with sea salt and pepper, to taste. Divide finished pasta between 2 dishes. Garnish with parmesan cheese.