Preheat a grill or grill pan to medium-high.
Place ingredients for gazpacho in a high-powered blender (or do in 2 batches in food processor). Process to desired consistency.
In a mixing bowl, season shrimp with salt and pepper. Add tequila, lime juice, garlic, olive oil and Tabasco, and toss to coat. Grill shrimp 3 minutes on each side until shrimp are pink, firm and browned at edges. Grill lime halves cut-side down to mark then squeeze over shrimp.
Serve gazpacho in bowls or chilled frosted mugs with grilled shrimp alongside for dipping.