Combine flour, milk, water, eggs, and melted butter in a large bowl; beat with a wire whisk until crepe batter is free of lumps.
Heat a nonstick skillet over medium heat. Pour 1/4 cup of batter into the skillet; cook until bubbles form on the surface, 2 to 3 minutes. Flip and cook crepe for 1 minute on the second side. Transfer to a plate. Repeat with remaining crepe batter.
Preheat oven to 350 degrees F (175 degrees C). Line a baking sheet with parchment paper.
Pour pinto beans into a small saucepan over medium heat; cook until heated through, about 5 minutes. Remove from heat and let cool slightly. Mash into a fine puree using a potato masher.
Combine salsa, tomatoes, corn, ginger, and chili powder in a large bowl. Mix in pureed beans. Spoon some of the bean mixture into the center of each crepe. Roll up crepes, tucking ends in neatly.
Place filled crepes seam-side down on the lined baking sheet. Sprinkle grated Monterey Jack cheese on top.
Bake in the preheated oven until cheese is melted, about 10 minutes.
