2 balls fresh burrata cheese, at room temperature (or sub for your favourite cheese)
Heat a large, high sided skillet over medium heat. Add the olive oil, chickpeas, and rosemary, and cook, stirring occasionally until the chickpeas are crisped all over, about 8-10 minutes. It’s OK if some of the chickpeas are popping. Add the lemon and cook another minute, until fragrant. Remove the chickpeas, rosemary, and most of the lemon from the oil to a paper towel-lined plate. Season with salt and pepper. Set the skillet aside.
Bring a large pot of salted water to a boil. Add the pasta and cook according to package directions until al dente. Just before draining, remove 1 cup of the pasta cooking water and save for later. Drain the rest of the pasta.
Meanwhile, place the skillet with the rosemary-infused oil still inside over high heat. When the oil shimmers, add the tomatoes, garlic, and a pinch each of salt, pepper, and red pepper flakes. Cook until the tomatoes begin to pop, about 4-5 minutes. Reduce the heat to low, add the vinegar, preserves or honey, and a splash of the pasta cooking water (about 3-4 tablespoons). Simmer 5-10 minutes, until the sauce reduces and is “jammy”.
Add the pasta, kale, and basil, tossing to combine. Crumble in the fried rosemary, reserving 1 sprig for topping, if using fresh. If needed, thin the sauce with additional pasta cooking water.
Divide the pasta and butter (if using), among plates and top with burrata cheese, crisp chickpeas, crumbled rosemary, and lemon.