Finely grate 1 whole garlic clove into a medium bowl. Add 1 large egg yolk, 1 tsp. fresh lemon juice, and ½ tsp. Diamond Crystal or ¼ tsp. Morton kosher salt and whisk to combine. Gradually stream in ½ cup extra-virgin olive oil, whisking constantly until aioli is light and thickened. Whisk in remaining 1 Tbsp. fresh lemon juice and season with salt. Set aioli aside.

Pat 1 lb. tail-on large shrimp, peeled, deveined, dry with paper towels; season with salt and set aside.

Heat ⅓ cup extra-virgin olive oil in a large skillet over medium-high. Working in 2 batches and adding more oil between batches if needed, cook 4 thick slices crusty bread until golden brown and crisp, 1–2 minutes per side. Transfer to plates; wipe out pan.

Heat 2 Tbsp. extra-virgin olive oil in same pan over medium-high. Arrange reserved shrimp in a single layer and cook, undisturbed, 2 minutes. Continue to cook, tossing occasionally, until just opaque, about 2 minutes more. Transfer to a plate.

Add remaining 2 Tbsp. extra-virgin olive oil to same pan, then add 2 pints cherry tomatoes in a single layer. Cook, undisturbed, until blistered underneath, about 4 minutes. Add 3 garlic cloves, thinly sliced, 1 Tbsp. sherry vinegar or red wine vinegar, 1½ tsp. smoked paprika, 1 tsp. ground cumin, ½ tsp. mild red chile flakes, and remaining 2 tsp. Diamond Crystal or 1 tsp. Morton kosher salt. Cook, stirring occasionally, until combined and some tomatoes have burst, about 4 minutes. Add shrimp and cook, stirring to coat, until heated through, about 1 minute.

Spread a thick layer of aioli over each toast. Spoon shrimp mixture on top, then scatter chopped parsley over. Sprinkle with more mild red chile flakes.