In a large skillet, heat 1 tsp of olive oil over medium heat. Add 1/4 cup minced white onion and sauté until translucent, about 3-4 minutes. Stir in minced garlic and cook for another minute until fragrant.
To the skillet, add the chopped green chiles, drained and rinsed beans, shredded chicken, 1/4 cup water, chicken bouillon, and ground cumin. Stir until well combined and let everything cook for about 5 minutes, allowing the flavors to meld. Remove from heat and set aside.
In a separate saucepan, melt 1 tsp of butter over medium heat. Add 1/2 cup chopped white onion and sauté until soft. Sprinkle 2 tbsp of flour over the onions and stir to create a roux. Gradually whisk in 1 cup of reduced sodium chicken broth, mixing until the sauce thickens. Stir in the 7 oz can of chopped green chiles and chopped jalapeños. Finally, mix in 1/2 cup light sour cream until creamy and well combined. Season with kosher salt to taste.
Preheat your oven to 350°F (175°C). In a 9x13 inch baking dish, spread a thin layer of the creamy salsa verde on the bottom. Take an 8-inch flour tortilla, fill it with a generous amount of the chicken and bean mixture, and roll it up tightly. Place the rolled enchiladas seam side down in the baking dish. Repeat until all filling is used.
Pour the remaining creamy salsa verde over the top of the enchiladas, making sure they are well covered. Sprinkle 3/4 cup reduced-fat Mexican cheese on top. Bake in the preheated oven for 25-30 minutes, or until the cheese is melted and bubbly.
Once out of the oven, let the enchiladas sit for a few minutes. Garnish with chopped fresh cilantro or scallions. Serve warm and enjoy!