Season the chicken pieces with Italian seasoning, salt, and black pepper.
Heat 1 tablespoon olive oil in a large skillet over medium-high heat and add the gnocchi in a single layer. Cook for 4-5 minutes, stirring occasionally, until golden and crispy. Remove to a plate.
Add the remaining tablespoon of olive oil to the same skillet and add the chicken pieces. Cook for 6-7 minutes, stirring occasionally, until golden brown and cooked through.
Add the minced garlic and cook for 30 seconds until fragrant.
Return the gnocchi to the skillet along with cherry tomatoes and balsamic vinegar. Cook for 2-3 minutes until tomatoes begin to soften.
Remove from heat and immediately stir in the fresh mozzarella cubes and torn basil.
Sprinkle with Parmesan cheese and serve immediately while the mozzarella is still melty.