Char peppers over gas flame or in broiler until blackened on all sides. Wrap in paper bag and let stand 10 minutes. Peel and seed peppers. Process roasted peppers, spinach, cheese, nuts, garlic, and chipotle chilies in food processor.
Add oil to blend and process. Season with salt and pepper.
For garlic Sauce:
Bring stock and cream to a boil in a small saucepan. Add garlic and basil; simmer until sauce thickens slightly. Season with salt and pepper. Can be made a day ahead.
Preheat oven to 400 degrees. Place 1 phyllo sheet on work surface. Brush with melted butter. Fold in half crosswise. Brush with butter. Place 1 chicken breast in center of phyllo. Season with salt and pepper.
Spoon 1 teaspoon pesto over chicken. Sprinkle with 1/4 cup cheese. Insert chicken in phyllo by folding dough over chicken. Brush with butter. Repeat with remaining chicken.
Refrigerate remaining pesto for other use.
Bake chicken about 25 minutes.
Transfer to plates. Bring garlic sauce to simmer. Spoon over chicken.