In a large bowl, combine the white beans, 1 tablespoon oil and garlic. Using a fork, lightly smash the beans, mixing with the oil and garlic until blended. Add the red pepper, bread crumbs, Worcestershire sauce, egg and chives. Mix until blended.
Crumble the ground turkey and add it to the bowl, along with ½ teaspoon salt and a generous sprinkling of pepper. Gently mix with a fork or your hands until just blended. (Don't over-mix or the burgers will be tough.)
Fill a medium bowl with water, moisten your hands, and shape the meat into four patties about 3 inches in diameter and ¾-inches thick, dipping your hands to keep the meat from sticking to them.
Heat the remaining 2 tablespoons of oil in a large nonstick skillet over medium- heat. Cook the burgers until the bottoms are browned, 4 to 5 minutes. Flip the burgers and continue cooking until they're firm to the touch and register 165°F on an instant-read thermometer, another 5 to 8 minutes. Serve immediately on the toasted bread.