Preparation Heat 4 Tbsp. oil in a large deep-sided skillet over medium-high. Add capers and cook, swirling pan occasionally, until they burst and are crisp, about 3 minutes. Using a slotted spoon, transfer capers to a paper towel-lined plate; set aside. Reserve oil in skillet. Cook cauliflower in same skillet over medium-high heat, stirring frequently, until beginning to brown, about 3 minutes. Reduce heat to low and add garlic, 1 tsp. salt, and 1/2 tsp. pepper. Cover and cook until cauliflower begins to soften, about 4 minutes. Uncover and increase heat to high. Add chickpeas, 2 Tbsp. butter, and remaining 2 Tbsp. oil and continue to cook, stirring occasionally, until cauliflower and chickpeas are lightly browned, about 5 minutes. Meanwhile, cook pasta in large pot of boiling salted water, stirring occasionally, until al dente. Drain, reserving 1 cup pasta cooking liquid. Remove skillet from heat and add lemon juice, 1/2 cup pasta cooking liquid, and remaining 2 Tbsp. butter. Add pasta, tossing and adding more pasta cooking liquid as needed, until coated. Divide arugula and pasta among bowls, stirring to combine. Top with reserved crispy capers.