Bring a medium saucepan of salted water to a boil. Add the Broccolini and cook until crisp-tender, about 3 minutes. Drain and rinse with cold water; set aside.
Preheat the oven to 400 degrees . Line a baking sheet with parchment paper and set aside. In a medium skillet, heat 1 tablespoon olive oil over heat. Add the onion and cook, stirring, until softened, about 5 minutes. Transfer to a bowl and let cool. Stir in the ricotta, parmesan, egg, 3/4 teaspoon salt and 1/2 teaspoon pepper. Fold in the Broccolini and mozzarella.
Lay 1 phyllo sheet on a work surface and brush with olive oil. Repeat with 3 more sheets. Halve the phyllo stack lengthwise. Spoon 3/4 cup Broccolini mixture onto 1 stack, near a short end. Fold the right corner diagonally over the filling to make a triangle; continue folding diagonally until you reach the other end. Place the turnover on the baking sheet and brush with olive oil. Repeat with the remaining phyllo and filling to make 8 turnovers.
Bake the turnovers until golden and crisp, 20 to 25 minutes. Serve with the marinara sauce.