Char poblano chilies in 500 degree oven for 20 minutes, turning half way through. Enclose in paper bag 10 minutes. Peel chilies. Using small sharp knife, carefully slit chilies open along 1 side. Remove seeds, leaving stems attached.
Mix shrimp and next 6 ingredients in medium bowl. Season to taste with salt and pepper. Fill chilies with shrimp mixture, dividing equally. Pull up sides of chilies to enclose filling. Place stuffed chilies on baking sheet. (Can be prepared 1 day ahead. Cover and refrigerate.)
Preheat oven to 350°F. Bake chilies uncovered until heated through and cheeses melt, about 15 minutes. Spoon 3 tablespoons Red Bell Pepper Sauce onto each of 8 plates. Place 1 stuffed chili atop sauce on each. Garnish with basil leaves, if desired, and serve.
RED BELL PEPPER SAUCE
Coarsely chop bell peppers.
Heat oil in medium skillet over medium heat. Add shallots, garlic, and chili; sauté until shallots are tender, about 5 minutes. Cool slightly. Transfer mixture to blender; add bell peppers and chicken broth. Puree until smooth. Season sauce to taste with salt and pepper. (Can be made 1 day ahead. Cover and chill. Rewarm over medium heat before serving.)