Pulse the baby arugula, walnuts, garlic, parmesan cheese, lemon juice, and olive oil in a food processor until a smooth, vibrant pesto forms.
Season the chicken breast with sea salt and black pepper, then sear in a non-stick skillet over medium-high heat for 6 minutes per side until golden and cooked through.
Remove the chicken from the skillet, let it rest for 3 minutes, then slice into thin strips.
Bring a small pot of salted water to a boil and cook the gnocchi for 2-3 minutes until they float to the surface, then drain.
In the same skillet used for the chicken, add the cherry tomatoes and sauté for 2 minutes until they begin to blister and soften.
Add the cooked gnocchi, sliced chicken, and prepared arugula pesto to the skillet with the tomatoes.
Toss everything gently over low heat for 1 minute to ensure the gnocchi is evenly coated and serve immediately.