1In a large, heavy skillet, heat a drizzle of oil over medium-high heat and saute the onion, carrot and celery for about 5 minutes, until soft. Add the butter and mushrooms and cook until the mushrooms release their liquid, then the vegetables start to turn golden. Sprinkle with flour and thyme and cook for another minute.
2Stir in the can of soup along with a can full of water, scraping up the browned bits on the bottom of the pan, and stirring until smooth. Bring to a simmer and cook for about 5 minutes, until thickened. (If it’s too thick, stir in another half or whole can of water.) Stir in the roasted chicken or turkey and peas and pour into a baking dish that will accommodate it.
3Preheat the oven to 400°F.
4To make the biscuits: In a large bowl, combine flour, baking powder, sugar and salt. Add the milk and canola oil and stir by hand just until you have a soft dough.
5On a lightly floured surface, pat or roll the dough into a 9” x 14” rectangle. Stir the garlic into the melted butter and spread over the dough, then sprinkle with cheese. Starting from a long side, roll tightly jelly-roll style into a log. Cut into 8-12 biscuits using dental floss or a serrated knife.
6Lay the biscuits on top of the chicken mixture, leaving a bit of space between them (they will rise in the oven), and bake for 30-40 minutes, until the the biscuits are puffed and golden brown and filling is bubbly. Let stand 10 minutes before serving.