Bring a large pot of salted water to a boil and add the angel hair pasta, cooking it according to package directions until al dente (usually 5-7 minutes). While the pasta cooks, mince your garlic cloves finely and set aside. Pat the shrimp dry with paper towels—this is crucial for getting a good sear and preventing them from steaming. Roughly chop the fresh parsley and have it ready for garnish. When the pasta is done, reserve 1 cup of the starchy pasta water before draining the pasta into a colander; don't rinse it.
Heat a large skillet over medium-high heat and add the butter and olive oil together—the combination gives you the best browning without burning the butter. Once the butter is foaming and the oil is shimmering, add the minced garlic and red pepper flakes, stirring constantly for about 30 seconds to 1 minute just until fragrant. I like to stop right before it starts to brown so the garlic stays sweet rather than bitter. This quick bloom will infuse the oil with incredible flavor.
Add the dried shrimp to the hot garlic butter in a single layer and let them cook undisturbed for 1-2 minutes on the first side until they turn pink and develop a light golden color. Flip each shrimp and cook for another 1 minute on the second side. Pour in the lemon juice and cover the skillet with a lid, then reduce heat to medium and cook for 2-3 minutes until the shrimp is completely cooked through and opaque. Remove the cooked shrimp to a plate, leaving the flavorful sauce in the skillet.
With the skillet still over medium heat and the garlic butter sauce still in the pan, add the spinach and reserved pasta water. Stir constantly for about 1 minute until the spinach is completely wilted and the liquid begins to emulsify slightly with the butter and oil. This pasta water is key—the starch in it helps create a silky sauce that coats the pasta beautifully.
Add the drained pasta from Step 1 directly to the skillet with the spinach and sauce. Stir in the freshly grated parmesan cheese until it melts and coats the pasta evenly. Return the cooked shrimp from Step 3 to the skillet and toss everything together gently to combine. I always taste at this point and adjust the seasoning with salt and pepper as needed—the pasta water and cheese are already salty, so go easy. Transfer to serving plates, garnish with the fresh parsley and a crack of black pepper, and serve immediately.