In a large skillet over medium-high heat, melt the butter. Add the minced shallots and sliced mushrooms. Cook, stirring occasionally, until the mushrooms release their liquid and it evaporates. Then, continue cooking until the mushrooms are deeply golden and dry, with no liquid remaining, about 8 to 10 minutes.
Reduce the heat to medium. Add the garlic and cook for 30 seconds, being careful not to let it burn.
Sprinkle the flour evenly over the mushroom mixture. Stir constantly for 1 to 2 minutes, until a thick paste forms. This will help thicken the gravy.
While stirring constantly, slowly pour in the chicken broth a little at a time, allowing each addition to fully incorporate before adding more. The mixture will thicken quickly.
Bring the gravy to a gentle simmer and cook for 3 to 5 minutes, stirring occasionally, until thick and glossy.
Reduce the heat to low. Slowly stir in the heavy cream. Do not boil after adding the cream; gentle heat keeps the gravy smooth and prevents it from breaking.
Stir in the soy sauce. Season to taste with salt and pepper.
Garnish with fresh thyme if desired. Serve warm.