Preheat your oven to 400°F. On a small baking sheet, toss the cherry tomatoes with olive oil, half the sea salt, and half the black pepper.
Roast the tomatoes for 12 minutes until the skins are blistered and slightly charred.
Season the chicken breast with the remaining salt and pepper. Heat a non-stick skillet over medium-high heat and sear the chicken for 5-6 minutes per side until the internal temperature reaches 165°F. Remove from the pan, let it rest for 5 minutes, and then slice into strips.
While the chicken rests, bring a pot of salted water to a boil. Cook the gnocchi according to the package directions (usually 2-3 minutes until they float). Drain, reserving 2 tablespoons of the cooking water.
In a small mixing bowl, whisk together the Greek yogurt, basil pesto, and lemon juice until a smooth, creamy sauce forms.
In the same skillet used for the chicken, combine the cooked gnocchi, fresh spinach, roasted tomatoes, and the pesto sauce. Stir over low heat until the spinach is just wilted, adding a splash of the reserved pasta water if the sauce needs thinning.
Add the sliced chicken back into the skillet, toss gently to coat everything in the sauce, and serve immediately.