Cook pasta as directed until it's al dente. Reserve ⅓ cup pasta cooking water. Drain pasta, and set aside.
In a large skillet over medium-high heat and add 1 tablespoon of olive oil. Once the oil starts to shimmer, place scallops in the skillet, flat side down. Do not overcrowd the pan; it might take you two batched. Cook until that side is deep golden brown, 2-3 minutes. Gently turn over; if they stick, cook another 30 seconds and try again. Cook on the second side until the scallop looks opaque in the middle and golden brown, another 2-3 minutes. Move scallops to a plate.
Pour out any oil in the skillet and place back on the burner over medium heat. Add butter and cook, swirling, until the butter browns, about 90 seconds, and then add garlic and saute for 30 seconds. Scrape off any brown bit at the bottom of the pan. Add pasta water, capers, spinach, and parmesan. Once combined, add lemon juice, then mix in the pasta.
Plate pasta topping it with scallops. Top with more parmesan.