Beat milk, eggs, and 1 1/2 tablespoons oil together in a bowl. Add flour and salt.
Heat the remaining oil in a skillet over medium heat. Pour in about 1/4 cup batter. Cook until brown, about 3 minutes; turn and continue cooking until other side is brown, about 2 minutes more. Remove crepe and cool. Repeat with the remaining batter.
Stir pepper Jack cheese, chicken, sour cream, green onions, jalapeno, garlic, chili powder, and cumin together in a bowl. Spoon 1/2 cup of the mixture onto the center of each crepe. Roll and place, seam-side down, in a single layer in a shallow 9x13-inch baking pan. Sprinkle remaining pepper Jack cheese on top.
Bake in the preheated oven until bubbly and golden brown, 20 to 30 minutes.