Toss chicken with 1/2 teaspoon salt, 1/2 teaspoon pepper, and Italian seasoning (1 tablespoon) and coat evenly.
Heat the oil (1 tablespoon) over medium-high heat in a large skillet. When the oil shimmers add chicken in a single layer (work in batches if necessary) and cook, stirring occasionally, for 3-4 minutes or until it begins to brown. (It doesn't need to be completely cooked at this point). Transfer browned chicken to a plate.
Melt the butter (2 tablespoons) in the skillet and sauté shallots (3 tablespoons), over medium-low heat, until translucent, about 4-5 minutes. Add garlic (1 tablespoon) and continue to sauté until fragrant, about 1 minute.
Stir in tomato paste (2 tablespoons) and cook, stirring so tomato paste doesn't burn, for 2-3 minutes.
Add wine (1/4 cup) to shallots and garlic and bring to a boil. Scrape the bottom of the pan to lift up any brown bits on the bottom. Continue to cook until the wine has reduced into syrup.
Stir in the chicken broth (1 cup), heavy cream (1 cup), sugar, and gnocchi (16 ounces) then simmer, adjust heat as needed, until the sauce is reduced and thickened, and the gnocchi is tender about 5 minutes.
Return the chicken to skillet along with any juices that have accumulated. Add sun dried tomatoes (3/4 cup) and Parmesan (3/4 cup), and stir to combine. Heat until parmesan has melted and chicken is heated through.
With the heat on low, stir in spinach (2 cups) and cook until the spinach wilts to your liking. Adjust seasoning if needed. Serve immediately.