Preheat the oven to 425°F.
In a large oven-safe skillet, heat the avocado oil over medium-high heat. Add the ground chicken and use a wooden spoon to break it into bite-size pieces. Cook, stirring occasionally, until the chicken begins to brown, about 3 minutes.
Add the chopped onion and minced garlic. Stir to combine and continue cooking until the chicken is fully cooked and the onion is translucent, about 4 minutes.
Add the crushed tomatoes, Italian seasoning, parsley, white sugar, and chicken stock. Season with freshly ground black pepper and stir to combine.
Add the uncooked pasta directly into the skillet and stir well. Bring the mixture to a boil over high heat. Once boiling, reduce heat to medium-low to maintain a gentle simmer. Cook, stirring occasionally, until the pasta is slightly tender and most of the liquid has reduced, about 7–9 minutes.
In a medium bowl, combine the cottage cheese, 2 tablespoons of the Parmigiano-Reggiano, ¼ teaspoon salt, and ¼ teaspoon black pepper. Stir to combine and set aside.
Stir the pasta mixture once more to ensure nothing is sticking to the bottom. Remove from heat.
Dollop the cottage cheese mixture evenly over the pasta. Top with shredded mozzarella and the remaining Parmigiano-Reggiano.
Transfer the skillet to the oven and bake for 15–20 minutes, until the sauce is bubbly and the cheese is melted.
If desired, broil for 1 minute for a more golden, lightly crispy top, watching carefully to prevent burning.
Remove from the oven and let rest for 5 minutes. Garnish with fresh basil before serving.