To prepare filling, heat oil in a large saucepan over medium-high heat. Add onion, carrot, and celery; sauté 4 minutes. Add garlic; sauté 30 seconds. Weigh or lightly spoon 1.1 ounces (1/4 cup) flour into a dry measuring cup; level with a knife. Stir flour, salt, and pepper into vegetables; cook 1 minute, stirring constantly. Stir in stock; bring to a boil. Reduce heat to medium; simmer 8 minutes, stirring occasionally. Stir in chicken and peas; simmer 5 minutes. Remove from heat. Remove rosemary from herb package; reserve for another use. Strip leaves from stems of remaining herbs; chop leaves to measure 2 tablespoons. Stir herbs into filling. Pour filling in a 2-quart baking dish or cast-iron skillet coated with cooking spray.
To prepare biscuits, weigh or lightly spoon 4.5 ounces (1 cup) flour into a dry measuring cup; level with a knife. Combine flour and baking soda. Using a pastry blender or 2 knives, cut butter into flour mixture until it resembles coarse meal. Stir in buttermilk. Turn dough out onto a lightly floured surface; knead gently 5 to 6 times. Roll to a 9-inch circle. Cut with a 2-inch round biscuit cutter, rerolling scraps. Arrange biscuits over filling; coat with cooking spray. Bake at 425° for 35 minutes or until browned.