Make gazpacho: Combine ¼ cup olive oil, garlic, and scallions in a small skillet. Cook over low heat until mixture sizzles. Let sizzle for 30 seconds, then transfer to a blender. Add cucumber, bell pepper, strawberries, parsley, and 1 cup vegetable juice and blend until smooth. Add more vegetable juice until you reach desired consistency. Blend in honey, vinegar, and coconut aminos; season with salt and pepper to taste.
Place soup in a large container and refrigerate for at least 12 hours, but up to 24. Taste and season again before serving.
Before serving, cook shrimp: Preheat oven to 400 degrees F. Line a large baking sheet with parchment paper. In a bowl, toss shrimp with 1 tablespoon olive oil, ¼ teaspoon salt, and ¼ teaspoon pepper. Roast, turning once, until just cooked through, 8 to 10 minutes. Transfer to a cutting board and let cool.
Just before serving, chop shrimp and avocado. Divide soup among 4 bowls and garnish with shrimp and avocado. Drizzle over a little extra olive oil, top with some pepper, and serve.