Place the ground chicken in a bowl with the scallions, parsley, dill and paprika; season with salt and pepper. Combine the mixture with a fork and form into four 1-inch thick patties.
In a heavy nonstick skillet, heat the EVOO, one turn of the pan, over medium-high heat. When the EVOO is hot, add the burgers and cook for 6 minutes on each side.
Pre-heat the broiler.
Place the red peppers, sour cream and shallot in a food processor. Process until smooth, about 20 seconds. Transfer to a small dish.
Toast the rolls under the broiler and spread lightly with softened butter. Slather the rolls with the red pepper sauce. Set a burger on each bun bottom and top with the radish and cucumber slices, two lettuce leaves and the roll top.