Make pistou: In a blender, whirl oil, lemon zest, and salt on high speed. Add basil and blend 15 seconds. Taste and adjust seasonings. Pour pistou into a bowl and cover with plastic wrap, pressing it against surface to prevent pistou from oxidizing. Chill.
Preheat a grill to medium (350° to 400°). Rinse shrimp and pat dry between paper towels, then put in a large bowl and toss gently with 1 tsp. each salt and pepper, chile flakes, and olive oil. Grill, turning once, until pink, curled, and just barely opaque in center, 5 to 6 minutes total, transferring to a large bowl as done.
Meanwhile, brush cut sides of lemons with a bit of oil and sprinkle lightly with salt. Grill lemons, cut side down, until charred, 1 to 2 minutes. Squeeze juice of 2 lemons over shrimp.
Arrange shrimp on a platter with remaining lemon halves and drizzle with pistou. Top with pea shoots.
MAKE AHEAD Pistou, up to 1 day, chilled.
*Very cold oil keeps the basil from heating up in the blender, thereby preserving its bright color.