Preheat the oven to 375°F (190°C) and lightly grease or spray a 9x13-inch baking dish.
In a medium skillet over low heat, warm 1 tsp olive oil. Add 1/4 cup minced onion and 2 minced garlic cloves; sauté until softened, about 2–3 minutes.
Add the 4.5 oz can chopped green chiles, 15.5 oz can beans (undrained or drained per preference), 1/4 cup water, 1 chicken bouillon, and 1 tsp ground cumin to the skillet. Stir, cover, and simmer on low for 15 minutes.
Remove the cover, stir in the 8 oz shredded chicken, and cook 4–5 more minutes until mixture thickens slightly; then set the filling aside.
In a large nonstick pan over medium heat, melt 1 tsp butter. Add 1/2 cup chopped onion and cook until translucent, about 3–4 minutes.
Stir in 2 tbsp flour and cook 1 minute while stirring. Gradually whisk in 1 cup reduced-sodium chicken broth until smooth, then simmer 4–5 minutes until the sauce thickens.
Stir in the 7 oz can chopped green chiles, 2 chopped jalapeños, and salt to taste. Cook 1 more minute, remove from heat, and stir in 1/2 cup light sour cream to make the enchilada sauce.
Spread about 1/4 cup of the enchilada sauce on the bottom of the prepared baking dish.
Place about 1/3 cup of the chicken and white bean filling into each 8-inch tortilla, roll up, and place seam-side down in the baking dish. Repeat with remaining tortillas and filling.
Pour the remaining enchilada sauce over the rolled enchiladas and sprinkle evenly with 3/4 cup reduced-fat Mexican cheese.
Cover the dish with aluminum foil and bake 20–30 minutes until heated through and the cheese is melted. Remove foil and top with chopped fresh cilantro or scallions before serving.