Arrange oven rack 6 inches from broiler; heat broiler. Arrange tomatillos and jalapeño, cut sides down, on a foil-lined baking sheet along with onion and broil until blistered, 10 to 12 minutes. Let vegetables cool, then transfer to food processor. Add lime juice, cilantro and 1/4 teaspoon salt, and pulse to combine (salsa should be slightly chunky).  Beat eggs with 1 tablespoon water and 1/4 teaspoon salt. Heat oil in large nonstick skillet on medium. Add eggs and cook, stirring with rubber spatula every few seconds, to desired doneness, 2 to 3 minutes for medium-soft eggs. Fold in 1/2 cup cheese.  Spread 1/4 cup beans on each tortilla, then divide eggs and remaining cheese on top. Spoon 2 tablespoons salsa over each and roll, folding sides over filling and then rolling from the bottom up. If desired, crisp both sides in nonstick skillet on medium. Serve with remaining salsa.