Preheat a non-stick skillet over medium heat. Season the chicken breast with a pinch of salt and pepper, then grill or pan-sear until fully cooked (around 4-5 minutes per side) before slicing into strips.
Peel and steam or boil the sweet potato until tender. Mash the sweet potato until smooth.
In a mixing bowl, combine the mashed sweet potato with the flour, cracked egg, and a pinch of salt. Mix until a soft dough forms. If too sticky, add a tiny bit more flour, being mindful not to overwork the dough.
Lightly dust a work surface with flour, then roll portions of the dough into small logs. Cut into bite-sized pieces to form the gnocchi.
Bring a pot of salted water to a boil. Gently drop the gnocchi into the water. Once they float to the surface, let them cook for an additional 1-2 minutes before removing with a slotted spoon.
In the skillet used for chicken, melt the butter over medium heat. Once melted, add the fresh sage leaves and let the butter simmer until it turns light brown with a nutty aroma, ensuring the sage crisps up slightly.
Add the cooked gnocchi to the sage brown butter, tossing gently to coat and allow them to crisp slightly on the edges.
Plate the gnocchi and top with the sliced grilled chicken. Drizzle any remaining brown butter over the dish and finish with an extra pinch of salt and black pepper, if desired.