Heat butter in Dutch oven over medium-high heat until hot. Add onion, garlic, thyme, sage and pepper. Cook and stir 3 to 5 minutes until onion is tender. Add flour, cook and stir 1 to 2 minutes. Whisk in broth; cook, whisking 4 to 6 minutes or until sauce boils and thickens. Stir in vegetables; cook 5 to 7 minutes or until vegetables are tender. Stir in rice, chicken and parsley; cook, stirring 2 to 3 minutes more. Place in 2.5 quart casserole.
Combine baking mix, buttermilk and green onions in medium bowl. Gently stir, just until dough comes together. Form dough into 9-inch long log on lightly floured surface; cut crosswise into 6-1/2-inch rounds. Or roll out dough on lightly floured surface to 1/2-inch thickness and cut with different shaped cookie cutters. Or top casserole with biscuits, spacing evenly.
Bake in 425-degree oven for 20 minutes until filling is bubbly and biscuits are golden brown. Serve immediately.
*1 can of store-bought biscuits can be used in place of homemade; top with green onions.
May be prepared 1 day ahead. Cover and refrigerate. Bring to room temperature before baking.