Prepare the broccoli by cutting off the stems, removing the tough outer skin, and cutting them into pieces. Cook the stems in salted water for 8 to 10 minutes.
Prep the broccoli florets by cutting them into small pieces. Cook the florets in boiling water for 2 to 3 minutes.
Save half a cup of the cooking liquid and remove the vegetables from the water. Cook spinach in the same water for about 20 seconds.
Cook the pasta until al dente, reserving some pasta water before draining.
In a pan, combine red pepper flakes, lemon zest, garlic, capers, softened butter, black pepper, and the reserved cooking liquid. Cook over low heat.
Add the drained pasta to the sauce, allowing it to absorb and emulsify with the starch from the pasta water.
Adjust seasoning to taste with salt and pepper. Serve with grated Parmesan or pecorino cheese on top.
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