Toast the eight ½‑inch‑thick slices of bread and set them aside, kept warm if possible.
In a large bowl, combine the rinsed, drained white beans, 1 tablespoon of the olive oil, and the minced garlic. Use a fork to lightly smash the beans and mix until the beans, oil, and garlic are evenly blended (mixture should be mashed but not completely puréed).
Add the finely diced red bell pepper, plain dried bread crumbs, Worcestershire sauce, egg, and chopped chives to the bowl. Stir until evenly combined.
Add the ground turkey to the bowl. Season with kosher salt and freshly ground black pepper to taste. Gently mix with a fork or your hands until just blended—do not overmix.
Fill a medium bowl with water and keep it nearby. Moisten your hands with the water and shape the mixture into four patties about 3 inches in diameter and ¾ inch thick, dipping your hands in the water as needed to prevent sticking.
Heat the remaining 2 tablespoons olive oil in a large nonstick skillet over medium heat.
Add the patties to the skillet and cook until the bottoms are browned, about 4 to 5 minutes. Flip the patties and continue cooking until they are firm to the touch and register 165°F on an instant‑read thermometer, about another 5 to 8 minutes.
Transfer the cooked burgers to the toasted bread slices and serve immediately.