Combine garlic, parsley, 1 tablespoon oil, a pinch of salt, and 1/2 cup water in a small saucepan. Add peas and cook over medium heat, stirring occasionally, until peas are tender, about 5 minutes for fresh peas, about 2 minutes for frozen. Drain; *RESERVE* the cooking liquid.
Transfer pea mixture to a food processor; pulse until a coarse paste forms. Transfer to a medium bowl; mix in chives, preserved lemon peel, lemon juice, Aleppo pepper, and 2 tablespoons olive oil. Stir in reserved cooking liquid by tablespoonfuls until mixture is still thick but spreadable. Season pea mash with salt, black pepper, and more lemon juice, to taste if desired.
Drizzle toast with oil; top with pea mash, sprinkle with remaining 1/2 tablespoon preserved lemon peel and more Aleppo pepper, and drizzle with more olive oil.