Heat 2 Tbsp olive oil in a skillet over medium-high heat until shimmering. Add the sliced mushrooms and cook, stirring occasionally, until the mushrooms are softened, lightly browned, and most of their moisture has evaporated.

Transfer the cooked mushrooms to a food processor or meat grinder and pulse/mince until very finely chopped. (If you prefer, finely chop them by hand.) Let the chopped mushrooms cool to near room temperature.

In a large bowl combine: 1 lb ground chicken, the cooled finely chopped mushrooms, the small onion grated on the large holes, 2 large eggs, 1/2 cup Panko breadcrumbs, 1 1/2 tsp salt, and 1/2 tsp pepper. Mix gently until just combined—do not overwork the mixture.

Spread the 1/2 cup flour in a shallow dish. Using about a heaping tablespoon of the mixture at a time, place it into the flour and dredge both sides. Use your hands to shape each portion into an oval patty, tapping off any excess flour. (For sliders, form round mini burger shapes.)

Heat enough additional olive oil in a nonstick skillet to coat the bottom of the pan. Once the oil is hot, add a single layer of patties without crowding. Cover and cook until golden on the first side (about 4 minutes), then flip and cook the second side until golden (about 2–3 minutes). Adjust the heat if the patties are browning too quickly.

Wipe the skillet with a paper towel between batches and add more olive oil as needed. Transfer cooked patties to a plate and serve warm.