Preheat the oven: Preheat the oven to 400°F and lightly grease a 9x13-inch baking dish.
Boil the shells: Bring a large pot of salted water to a boil. Cook jumbo pasta shells 1–8 minutes
less than the package directions so they're al dente and hold their shape. Drain, rinse with cool water, and toss with a little of the 1 tablespoons olive oil so they don't stick.
Brown the chicken: Heat the rest of the olive oil in a large skillet over medium-high heat. Add 2 pounds ground chicken (thigh or 93% lean) and let it sear undisturbed for 2–10 minutes
to get real browning, then add 2 teaspoons Italian seasoning, 1 teaspoons garlic powder, and 1 teaspoons salt (for chicken). Break into small crumbles and cook until no pink remains. Work in two batches if your skillet is crowded, so the chicken browns instead of steaming.
Wilt the spinach: Add 5 ounces fresh spinach to the skillet with the chicken and stir just until wilted. Transfer to a large bowl, let cool slightly, and pour off any liquid that collects so the filling isn't watery.
Make the filling: Blend 2 cups cottage cheese (2% or 4%) until completely smooth. Add it to the chicken and spinach along with 1 cup part-skim ricotta, 0.5 cups grated Parmesan (for filling), 1 large egg, salt (for filling), and black pepper. Mix well, then taste and add a pinch more salt if needed.
Make the pumpkin-marinara sauce: Whisk together 15 ounces pumpkin purée (not pie filling), marinara sauce (simple, low-sugar), milk, garlic cloves, minced,Parmesan (for sauce), and salt (for sauce) until smooth and creamy. If it's too thick to spoon easily, add another splash of milk.
Assemble: Spread about 1 cup of sauce over the bottom of the baking dish. Stuff each shell generously with filling (about 3 tablespoons) and nestle them snugly in a single layer, open-side up. Dollop any leftover filling into the gaps between shells. Spoon the remaining sauce over and around the shells.
Bake covered: Cover the dish tightly with foil and bake until the sauce is bubbling around the edges.
Add cheese and finish: Remove the foil, sprinkle 1.5 cups shredded mozzarella over the top, and bake uncovered until the cheese is melted, bubbly, and starting to brown.
Rest and serve: Let the shells rest for 10 minutes