Preheat oven to 375℉.
Pat salmon with paper towel, sprinkle with salt and pepper. Drizzle with olive oil and bake for 20 minutes. The salmon should flake easily and internal temperature is 145℉. Remove from oven and break into pieces with fork and set aside.
Meanwhile, bring a sauce pot of water to a boil, add salt and cook pasta according to the package instructions. Reserve 1/2 cup of pasta water, then drain.
Using a skillet, over medium heat, melt butter and add garlic, sauté for about 1 minute, long enough to release it's fragrant. Add and whisk together lemon juice, heavy cream, thyme, 1/4 cup of reserved pasta water and spinach. Cook for about 1 minute until the sauce starts to bind and thicken. Season with salt and pepper, and red pepper flakes is desired. Toss in the pasta and coat with sauce. Add more pasta water is needed. Add salmon pieces.
Serve immediately. Garnish with fresh thyme and parsley.