In a large bowl, combine 2 pounds ground chicken breast, 1/2 cup chopped onion, 1/2 cup shredded zucchini, 1/2 cup seasoned bread crumbs, 1 egg, 1/2 teaspoon salt, and 1/2 teaspoon ground black pepper. Mix until all ingredients are evenly distributed.
Cover the bowl and let the mixture rest at room temperature for about 30 minutes to allow the bread crumbs to absorb moisture and firm the mixture.
After resting, shape the mixture into evenly sized patties about 1/2–3/4 inch thick and place them on a plate or tray.
Heat a large frying pan over medium to medium-high heat. Add 2 tablespoons cooking oil (olive or vegetable) and heat until the oil shimmers.
Add the patties to the pan in a single layer without overcrowding; cook in batches if needed. Cook the patties about 4 minutes per side, flipping once, until both sides are golden brown and the centers are cooked through (no pink remaining).
Transfer cooked patties to a paper-towel-lined plate to drain briefly.
Serve the croquettes warm with a dollop of sour cream and a sprig of fresh dill.