Fire-roast fresh pasilla chiles until blackened and blistered. Sweat in plastic bag. Remove skins. Slit chiles; remove seeds and veins, leaving stem ends intact. Fill with shredded pepper jack cheese. Press together gently to close slit. Mix tempura batter mix with water according to package directions. Dip chiles into tempura batter; deep-fry until golden-brown and crispy. Drain thoroughly. Serve with prepared salsa verde.