In a medium saucepan, melt butter over medium heat and add shallots and mushrooms. Cook, stirring occasionally, till softened, about 2-3 minutes. Then sprinkle flour in evenly and stir till combined, about 1 minute.
Stir in the stock, still over medium heat, and bring to a simmer. Continue to simmer, stirring occasionally until thickened, about 4-5 minutes. Add the cream, and fresh thyme leaves until combined. Bring back to a simmer about 2 minutes until the gravy is thickened and creamy. Add salt and pepper to taste. Serve warm.
Notes
For gluten free, use 2 tablespoons of cornstarch and whisk together with a little bit of broth before adding to the saucepan so it doesn't clump.
For dairy free, replace butter with ghee, olive oil, or vegan butter depending on what's best tolerated (vegan butter is not migraine-friendly). Use coconut cream or oatly instead of cream.