Preheat the oven to 425 degrees . In a large skillet, heat 1 1/2 tsp. olive oil over medium-high. Add the sausage and cook, breaking up with a spoon, until browned, about 4 minutes; transfer to a plate.
Reduce the heat to low. Add the fennel, garlic and the remaining 1 1/2 tsp. oil; season with salt and pepper. Cover and cook, stirring occasionally, until the vegetables soften, 5 to 7 minutes.
In a small bowl, beat the egg with 1 tsp. water. On a lightly floured surface, roll each puff pastry sheet into a 10-by-12-inch rectangle.
Transfer 1 sheet to a parchment-lined baking sheet. Top with an even layer of the sausage, then the vegetable mixture, leaving a 1-inch border. Using a tablespoon, dot with the ricotta, then drizzle with the marinara and sprinkle with half the basil. Brush the dough border with the egg and top with the remaining puff pastry, lining up the edges and pressing to seal. Brush the top with egg, then use the tines of a fork to crimp the edges. Cut 4 slits in the top to allow steam to escape. Bake until the pastry is puffed and golden, 20 to 30 minutes. Sprinkle with the remaining basil.