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1
Bring six quarts of generously salted water to a boil while prepping all of your sauce ingredients. When you add the pasta, start the sauce (see step 2). Cook pasta to al dente according to package instructions. Add the broccoli to the pasta during the last 2 minutes of cooking time. Alternatively, you can blanch the broccoli first until desired tenderness, remove it from your pot with a spider or large slotted spoon and set aside, then cook the pasta.
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2
In a large skillet or Dutch oven (large enough to hold a pound of cooked pasta and sauce) over medium heat, combine olive oil (1/4 cup total), anchovy, and garlic slices. Cook for about 2 minutes, or until the garlic sizzles and the anchovy melts into the oil, stirring a few times.
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3
Add the red pepper flakes in a hot spot and toast for a few seconds, then stir to combine with the anchovy and garlic. Repeat with the sun-dried tomatoes (drained from the rest of their oil), adding them to a hot spot and letting them toast for another minute or so before stirring to combine.
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4
Ladle 1 cup of boiling pasta water into the skillet and stir well. Keep the liquid at an active simmer to soften the tomatoes. Cook for a few minutes until the liquid has started to thicken.
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5
Stir in the cannellini beans, a pinch of salt, and another cup of boiling pasta water, and maintain an active simmer for another three or four minutes, or until the sauce has thickened.
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6
Drain the pasta and broccoli (reserving a cup of cooking water) and add them to the sauce once it's done. Toss well and add more pasta water if needed. Off the heat, toss in the cheese. Season to taste with the lemon zest, juice and salt. Finish the pasta with a drizzle of good-quality extra-virgin olive oil.
