Melt 1 tablespoon of unsalted butter over medium heat in a large pan. Add 2 minced garlic cloves and 2 diced poblano peppers, stirring occasionally for about 10 minutes.

Add 2 tablespoons of butter to the pan with the cooked peppers and garlic. Once melted, sprinkle in 1/4 cup of all-purpose flour, stirring continuously to form a paste and cook for about 1 minute.

Whisk in 2 cups of chicken broth gradually, ensuring the mixture is smooth. Simmer over medium heat, stirring frequently until it thickens slightly, about 5 minutes.

Pour in 1 cup of whole milk while stirring. Let it simmer for an additional 3-5 minutes. Stir in 1/4 cup of chopped cilantro and kosher salt to taste before removing from heat.

Preheat your oven to 375°F. Warm 8 corn tortillas in a dry skillet over medium heat for 30 seconds on each side.

Spread a thin layer of the creamy poblano sauce in a baking dish. Fill each warm tortilla with shredded chicken and roll tightly. Place seam-side down in the dish.

Drizzle the remaining creamy poblano sauce over the enchiladas and sprinkle 1 cup of shredded pepper jack cheese on top.

Bake for 15-20 minutes until the cheese is melted and bubbly.

Once out of the oven, squeeze fresh lime juice over the enchiladas and garnish with cilantro. Serve warm.