Preheat oven to 400F. Arrange baguette slices on a baking sheet and brush both sides with 2 tablespoons olive oil. Bake until golden and crisp, about 8 minutes, flipping halfway through. Set aside.

Pat shrimp completely dry with paper towels - this is crucial for browning. Heat remaining 1 tablespoon olive oil in a large skillet over medium-high heat until shimmering. Add shrimp in a single layer and cook without moving until pink on the bottom, about 2 minutes. Flip and cook until just opaque throughout, 1 to 2 minutes more. Transfer to a plate.

Reduce heat to medium. Add butter to the same skillet. Once melted, add garlic and red pepper flakes. Cook until fragrant and just starting to turn golden, 30 to 60 seconds - do not let it brown. Remove from heat immediately and stir in lemon juice, salt, and pepper.

Return shrimp to the skillet and toss to coat in the garlic butter. The residual heat will finish cooking them gently.

Halve and pit avocados. Scoop flesh into a bowl and mash roughly with a fork, leaving some chunks. Season lightly with salt.

Spread a generous layer of mashed avocado on each toast. Top with 2 to 3 shrimp and drizzle with the garlic butter from the pan. Sprinkle with parsley and serve immediately while the shrimp are warm.