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Step 1
Use a peeler to shave the outer fibrous layer of the broccoli stalks. Slice off the bottom inch or so of the stalk that is very tough. Then thinly slice the stalks into coins and set aside. Cut the crowns into florets (not too big or too small).
Step 2
Cook the pasta. Bring 8 cups (2.1L)** of water in a saucepan to a boil. Once the water is nearly boiling, add a tablespoon of kosher salt. Add the pasta, and once it returns to a boil, start the timer and cook according to the package’s minimum time for al dente pasta, stirring occasionally.
Step 3
About 3 minutes before the pasta timer is done, add broccoli florets (not the stems). Cook until the pasta is barely al dente (a little undercooked is okay) and florets are crisp-tender and bright green. Scoop out 1 cup of pasta water, then drain the pasta and broccoli (do not rinse).
Step 4
While the pasta water is heating up or pasta is cooking, make the sauce***. Zest the lemon with a microplane or citrus zester, then juice the lemon. In a small or medium bowl, whisk together the tahini, olive oil, 2 tablespoons of the lemon juice, maple syrup, ½ teaspoon kosher salt, and a generous amount of pepper. Add a pinch of the lemon zest but save the rest for topping. Whisk until the sauce is well-combined and thick. Stream in ice water and keep whisking until creamy but pourable (about 4 tablespoons).
Step 5
Meanwhile, make the topping: combine the slivered basil with the reserved lemon zest and the flaky sea salt.
Step 6
While the pasta is cooking, heat the 2 ½ tablespoons of olive oil in a deep sauté pan over medium-high heat. Once hot, add the broccoli stems with a few pinches of salt. Cook for 2 minutes, then add the shallots and garlic, and cook for another 2 to 4 minutes, until broccoli stems have some color and shallots are golden. Add the red pepper flakes and cook for 30 seconds.
Step 7
Assemble the pasta. Add the hot cooked pasta and broccoli to the shallot-broccoli stem mixture, along with the tahini sauce and ¾ cup (180 mL) pasta water. Keep the pan over medium-high heat and use tongs to vigorously toss everything together, until the sauce is emulsified and clings to the pasta, and the pasta is al dente, about 2 minutes. If needed, add a bit more pasta water to bring everything together.****
Step 8
Take the pasta off the heat. Stir in most of the basil topping and toss to coat. Taste, adding more salt or pepper to season and a bit of the remaining lemon juice, if desired. Just before serving, garnish with remaining topping.