Melt butter and pour into the bottom of a slow cooker. Add mixed vegetables, sliced mushrooms, garlic, parsley, thyme, rosemary, celery seed, salt, pepper and ricemilk. In a separate bowl, whisk together broth and flour. Pour over vegetables in the slow cooker and stir to combine everything. Cover and cook on high for 4 hours.
After 4 hours, adjust the racks in your oven so that it can accommodate your slow cooker crock*. Preheat the oven to 350°F. Stir and check the thickness of the sauce. If it’s too thin, spoon out a couple of tablespoons of liquid into a bowl. Whisk cornstarch into hot liquid until dissolved. Add cornstarch mixture back to slow cooker and stir to combine.
Separate biscuit dough into individual biscuits. Top mixture in slow cooker with biscuits. Bake slow cooker crock, uncovered, 35 to 40 minutes, until biscuits are deep golden brown and cooked through. Let stand 5 minutes before serving.
*If your slow cooker crock is not removable or is not ovenproof, bake biscuits separately according to package directions. Split biscuits, arrange in bowls and spoon pot pie filling over them.