Preheat your oven to 400 degrees Fahrenheit.
In a large bowl, toss the thawed shrimp with olive oil, salt, pepper, paprika, chili powder, and minced garlic until coated.
Arrange the seasoned shrimp in a single layer on a large sheet pan. Bake for 10-13 minutes or until the shrimp is cooked through, pink, and opaque. Set aside.
In a deep pot (4.5 quarts), combine the pasta, cherry tomatoes, salt, pepper, oregano, and thyme. Pour in the vegetable broth and bring it to a boil over medium-high heat.
Cook the pasta for 9-11 minutes or until it reaches al dente texture.
Turn off the heat and add a heaping spoonful of pesto, heavy cream, and fresh spinach to the pot. Mix everything together while the pot is still hot, allowing the spinach to wilt naturally without becoming too soggy.
Serve immediately in your favorite pasta bowl and top it with the delicious baked shrimp. Enjoy your delightful and easy-to-make pesto pasta with a touch of coastal goodness!