How to Make It
Broil jalapeño on a foil-lined baking sheet, turning, until charred, 7 to 9 minutes. Transfer to a bowl, cover, and let steam for 5 minutes; peel, stem, and seed jalapeño.
Cook snap peas in a pot of boiling salted water until crisp-tender, about 2 minutes. Remove with a slotted spoon. Add English peas to pot and cook until tender, 3 to 4 minutes. Reserve ¼ cup cooking water; drain.
Place English peas in a food processor. Add jalapeño, parsley, reserved cooking water, 2 tablespoons oil, 2 teaspoons lemon zest, 2 tablespoons lemon juice, half the garlic, and several grinds of pepper. Process until smooth, scraping sides of bowl as needed.
Toss shrimp with thyme, several grinds of pepper, and remaining garlic, 2 tablespoons oil, 1 teaspoon lemon zest, 1 tablespoon lemon juice, and ½ teaspoon salt. Transfer to prepared baking sheet and broil, flipping once, until opaque, 1 to 2 minutes per side.
Serve shrimp over pea puree. Top with snap peas, pea shoots, and a drizzle of oil.