Tuscan Chicken Gnocchi

1 medium shallot
3 cloves garlic
1/2 cup drained oil-packed sun-dried tomatoes (2 1/2 ounces)
1 ounce Parmesan cheese (1/2 cup firmly packed freshly grated or 1/3 cup store-bought grated)
1 1/2 pounds boneless, skinless chicken thighs (about 6)
1 teaspoon kosher salt, divided
1/2 teaspoon freshly ground black pepper, plus more for serving
2 tablespoons olive oil, divided
1 tablespoon all-purpose flour
2 cups whole or 2% milk, plus more as needed
1 pound shelf-stable potato gnocchi
3 packed cups baby spinach (about 3 ounces)

Finely dice 1 medium shallot (about 1/4 cup). Mince 3 garlic cloves. Thinly slice 1/2 cup drained oil-packed sun-dried tomatoes. Finely grate 1 ounce Parmesan cheese (about 1/2 packed cup) if needed, or measure out 1/3 cup store-bought grated.
Pat 1 1/2 pounds boneless, skinless chicken thighs dry with paper towels. Season all over with 1/2 teaspoon of the kosher salt and 1/2 teaspoon black pepper.
Heat 1 tablespoon of the olive oil in a 12-inch cast iron or high-sided nonstick skillet over medium-high heat. Add the chicken in a single layer and cook until deeply browned and an instant-read thermometer inserted into the thickest part registers 165°F, about 5 minutes per side. Transfer the chicken to a plate.
Reduce the heat to medium. Add the remaining 1 tablespoon olive oil and heat until shimmering. Add the shallot, garlic, sun-dried tomatoes, and remaining 1/2 teaspoon kosher salt. Cook until fragrant, about 1 minute. Sprinkle 1 tablespoon all-purpose flour evenly over the tomato mixture and cook until the flour begins to brown, 30 seconds to 1 minute. Add 2 cups whole or 2% milk and bring to a rapid simmer, stirring regularly.
Add 1 pound shelf-stable potato gnocchi (breaking the gnocchi apart if needed). Cook, stirring frequently, until the sauce is reduced slightly and thickened and the gnocchi is tender, about 3 minutes. Remove the skillet from the heat.
Add the Parmesan and 3 packed cups baby spinach. Stir until the cheese melts and the spinach wilts. If the sauce gets too thick, add more milk 1 tablespoon at a time until you reach the desired consistency. Nestle the chicken into the gnocchi mixture, and add any accumulated juices on the plate, before serving.

* For the amount of gnocchi in this, consider increasing the amount of chicken.  Something else that would be good in this is mushrooms.