Preheat oven to 375 degrees F (190 C).
In a large skillet over medium-high heat, melt butter. Add onion and sauté for 3 minutes or until softened. Stir in flour and cook for 1 minute, stirring constantly. Slowly add chicken broth, whisking constantly to prevent lumps from forming. Bring to a simmer and let thicken for 2 minutes.
Add half and half, thyme, rosemary, salt, and pepper. Stir to combine then add frozen vegetables and chicken. Simmer for 5 minutes or until heated through. Pour into a 9 x 13-inch baking dish.
In a medium bowl, whisk together flour, baking powder, baking soda, and salt. Cut in butter using a pastry blender or two forks until it resembles coarse crumbs. Stir in buttermilk until just combined.
Drop biscuit dough by large spoonfuls onto the filling. Sprinkle parsley over top and bake for 25-30 minutes or until golden brown and cooked through.
Serve warm.