If you want to serve over rice, use leftover rice or cook some now. (See How to Cook Brown Rice for instructions on cooking rice.) Prepare the rice (or pasta) to be ready around the same time as the shrimp.
For shrimp:
If using fresh shrimp, peel* and clean. If using frozen, peeled shrimp, thaw by placing in a baggie, then submerging it in a bowl of warm water for 30 minutes.
Place shrimp in a medium bowl, and add juice from the lemon half. Season with salt and pepper, then toss. Set aside while you follow the next steps.
For vegetables:
Chop onion, to yield no more than 1 cup. Mince garlic.
Melt butter in a large skillet over medium-low heat, then add onion and garlic. Cook and stir frequently 3 to 5 minutes, or until onions are soft and translucent.
While onion mixture cooks, chop tomatoes (should yield about 1-1/2 cups, or use canned). Add to onions, along with thyme and hot pepper sauce. Cook and stir another 3 to 5 minutes to reduce the liquids and intensify the flavor.
To assemble:
Add shrimp and simmer (uncovered) over low heat, stirring frequently for 3 to 5 minutes, or until shrimp is done.
Remove from heat and stir in the cream, half-and-half, or Greek yogurt. Add more hot sauce if desired.
Serve on top of rice and garnish with fresh parsley.