In a medium bowl, whisk the eggs with 6 Tbs. water until smooth.
Season with salt and pepper, if desired. Lightly coat an 8-inch nonstick skillet with cooking spray and heat over medium heat.
Pour ¼ cup of the egg mixture into the skillet, immediately swirling the pan to coat the bottom in a thin, even layer, just like a crêpe.
Cook for 2 to 3 minutes, until the egg is set. Gently slide the finished crêpe onto a plate lined with paper towels.
Place a paper towel on top and repeat with the remaining egg mixture to create 12 crêpes.
Set aside to cool.
Wipe out the skillet, coat it again with cooking spray, and return to medium heat.
Add the chopped onion and cumin, cover, and cook for 3 minutes until the onion has softened.
Stir in the pinto beans, garlic, and 1 cup (240 ml) of water or vegetable broth.
Cover and let it simmer for 5 minutes. Gently mash some of the beans with the back of a spoon to naturally thicken the sauce.
Stir in the cooked brown rice and ½ cup of the salsa.
Continue to cook for 5 more minutes, until most of the liquid has been absorbed.
Preheat your oven to 350°F (175°C).
Coat a large baking dish with cooking spray. Spoon about ¼ cup of the bean and rice filling down the center of each egg crêpe, roll it up, and place it seam-side down in the prepared baking dish.
Once all crêpes are filled and arranged, pour the remaining 1 cup (240 ml) of salsa over the center of the enchiladas and sprinkle evenly with the Monterey Jack cheese.
Bake for 15 minutes, or until the filling is heated through and the cheese is perfectly melted and bubbly.
