Preheat broiler with rack closest to heat. Set tomatillos on a foil-lined rimmed baking sheet. Broil, turning once, until blackened, 10-15 minutes. Purée in a blender. Set aside.
Preheat oven to 350° F.
Heat oil in a saucepan over medium heat, add shallot and cook until softened, 2 to 3 minutes. Add thyme, salt, and pepper and cook until shallot starts to brown, an additional minute. Add wine and reduce until almost gone, about 2 minutes. Stir in milk, sour cream, tomatillo purée, green chiles, and potato starch. Cook over medium-high heat, stirring often, about 5 minutes, then reduce heat and simmer until sauce thickly coats a wooden spoon, 3 to 5 more minutes. Set aside.
Empty tuna with all the juices into a medium bowl, and break any large chunks apart with a fork. As you mix, the tuna will soak up those juices. Add the crumbled queso fresco and the white beans to the tuna. Gently mix the tuna, cheese, and beans together. Set aside.
Make enchiladas: Heat a large cast iron skillet over medium-high heat. Working with 1 tortilla at a time, cook in dry skillet, turning once, until softened, about 30 seconds total. Lay tortilla flat on a work surface. Arrange tuna mixture down the center of the tortilla. Roll enchilada closed and place seam down in a 9 x13-inch baking dish (with no sauce on the bottom). Repeat procedure with remaining tortillas and filling. Pour green chile sauce over enchiladas.
Bake for 20 minutes or until sauce is bubbling.
Garnish with additional queso fresco, cilantro, red onion. Enjoy!