Preheat the oven to 425°F.
Toss chicken with 1 tablespoon olive oil, garlic powder, Italian seasoning, and salt.
Heat the remaining olive oil in a large, oven-safe skillet over medium-high heat.
Pan fry chicken for 8-10 minutes, flipping halfway, until golden and internal temperature is just below 165°F.
Transfer chicken to a board to rest. In the same pan, melt 1 tablespoon butter, add shallot, cook until soft. Add garlic, cook until fragrant.
Add remaining butter, sprinkle flour to create a roux. Whisk in broth, milk, and cream, cook until thickened.
Dice chicken, add to sauce with gnocchi. Sprinkle with cheeses.
Bake for 12-15 minutes until cheese is bubbly and golden.