1. Preheat broiler to high.
2. Heat a large skillet over medium-high heat. Coat pan with cooking spray. Add onion; sauté 4 minutes or until tender. Stir in chopped tomatoes, salsa verde, and 1/4 teaspoon salt; cook 15 minutes or until thickened, stirring frequently. Place tomato mixture in a food processor; add cilantro. Process mixture until smooth. Set aside.
3. Place poblanos on a foil-lined baking sheet; broil 3 inches from heat 8 minutes or until blackened and charred, turning after 6 minutes. Place in a paper bag; fold to close tightly. Let stand 15 minutes. Peel and discard skins. Cut a lengthwise slit in each chile; discard seeds, leaving stems intact. Spoon 1/4 cup Jack cheese and 1 1/2 teaspoons goat cheese in cavity of each chile.
4. Preheat oven to 350°.
5. Lightly beat egg yolks in a small bowl. Place egg whites in a medium bowl; beat with a mixer at high speed until stiff peaks form. Fold egg yolks into egg whites. Combine flour and black pepper in a shallow dish. Place cornmeal in another shallow dish. Dredge poblanos in flour mixture, and dip into egg mixture. Dredge in cornmeal.
6. Heat oil in a large stainless steel skillet over medium-high heat until hot; reduce to medium heat. Add coated poblanos to oil; cook 6 minutes or until crisp, turning to cook on all sides. Place chiles on a baking sheet, and bake at 350° for 8 minutes or until cheese melts. Serve with tomato sauce.