Prepare pasta according to package directions. Return to pan.
Meanwhile, for marinara sauce, in large saucepan, heat olive oil over medium heat. Add garlic; cook and stir 30 seconds. Add chopped tomato, diced tomatoes, salt, if desired, thyme, basil, ½ teaspoon red pepper flakes and brown sugar. Stir to combine. Increase heat; bring to boil. Reduce heat and simmer 5 minutes. Remove from heat. Blend sauce with immersion blender (or regular blender). Return sauce to saucepan; bring to simmer. Add Parmesan cheese; simmer 5 minutes.
Add thawed shrimp to sauce; heat through, about 2 minutes (do not overcook). Stir in parsley, thyme, garlic and red pepper flakes. Remove from heat. Toss with pasta. Serve immediately, sprinkled with chopped basil, as desired.
For spicier sauce, add additional crushed red pepper flakes, as desired. If desired, two cups prepared marinara sauce can be substituted for the homemade sauce.