Preheat oven to 375°. Roll pastry sheet out onto a large rimmed baking sheet (leaving parchment paper from package underneath). Fold over edges on each side to form a ½-inch border to hold in the filling. Whisk together milk and 1 teaspoon of the olive oil; brush mixture over base and edges of pastry.
Arrange sliced onions evenly over pastry, slightly overlapping. Drizzle onion with balsamic vinegar and 2 tablespoons of the olive oil; sprinkle with ½ teaspoon of the salt.
Bake in preheated oven until the pastry is crisp and golden, 25 to 30 minutes.
Meanwhile, heat remaining 1 teaspoon olive oil in a medium skillet over medium. Add spinach and chopped garlic; cook, stirring often, until spinach is wilted and just softened, about 2 minutes. Season with pepper and remaining ¼ teaspoon of salt. Drain any liquid.
Remove tart from oven. Arrange wilted spinach over onions and scatter peas over the top. Sprinkle with lemon zest and lemon juice. Slice and serve.
