Preheat the oven to 400°F (200°C) and lightly spray a 13x9-inch baking pan with cooking spray.
Heat the vegetable oil in a nonstick skillet over medium heat. Add the chopped onion and minced garlic and cook, stirring, until softened, about 2 minutes.
Add the tomato sauce, chicken broth, shredded chicken, 1/4 cup chopped cilantro, drained chopped pickled jalapeños, chili powder, cumin, oregano, and kosher salt to the skillet. Stir and simmer until the mixture has reduced slightly, about 4–5 minutes. Remove from heat.
Lay one tortilla flat and spread about 1 tablespoon of the soft goat cheese in a stripe down the center. Top with roughly 1/3 cup of the chicken mixture, then roll tightly and place seam-side down in the prepared baking pan. Repeat with remaining tortillas and filling.
Pour the enchilada sauce evenly over the rolled tortillas, then sprinkle the grated Mexican blend cheese on top. Cover the pan with aluminum foil.
Bake until heated through and the cheese is melted, about 20–25 minutes. For browned spots on the cheese, remove the foil for the last 5 minutes of baking.
Serve the enchiladas warm topped with additional chopped cilantro and a dollop of sour cream if desired.