Cut 6 tablespoons butter into 1/2-inch cubes, and refrigerate until ready to use. Melt 2 tablespoons butter in a medium nonreactive saucepan over medium-low. Add onion, sliced garlic, shiitake stems, tomato, black peppercorns, and bay leaf, and cook until vegetables are soft but not brown, about 12 minutes. Add balsamic vinegar
and 1/3 cup water, increase heat to medium-high, and cook, stirring occasionally, until mixture is syrupy, about 4 minutes.