Cook the pasta according to package directions, cooking it for the least amount of time recommended. You want it to be al'dente. When the pasta is done cooking drain it and set it aside.
Heat a large skillet over medium heat. Add the olive oil and the garlic and cook until the garlic starts to smell good, about 1 minutes.
Add the red pepper flakes, mushrooms, and diced tomatoes to the skillet. Cook until the mushrooms start to release their moisture, about 5 minutes. Add the baby spinach and stir to combine. Bring the mixture to a light simmer and add the shrimp. Cooke for 3-4 minutes, stirring often, until the shrimp is cooked through. It'll turn a creamy whitish pink when cooked.
Remove the pan from the heat and and add the marinara and then the Greek yogurt, stir to combine. Add the cooked pasta and stir to combine. The hot sauce will reheat the pasta, but if you need to put it back on the burner, over medium-low heat, for a minute or two to reheat the pasta then you can.
Serve the dish right away with the additional Parmesan on top.