Preheat the oven to 375°F. Butter an 8-inch round cake pan.
Combine the flour, sugar, baking powder, baking soda and salt in bowl of a food processor or large bowl. Add the butter and pulse in food processor, or cut the butter in with a pastry blender or 2 knives, until the mixture resembles coarse crumbs. Gradually add heavy cream and pulse in the food processor or stir the cream into the flour mixture in the bowl with a fork until just moistened.
Gather the dough into a ball and gently knead about 5 times on a lightly floured surface, just until the dough holds together nicely.
Place the dough into the prepared cake pan, press gently so that is fills the bottom of the pan evenly and relatively smoothly, taking care of the edges and making it as smooth as possible. Brush the biscuit with butter and sprinkle lightly with salt. Bake for 20 to 25 minutes or until top is golden. Let cool 5 minutes in the pan on a wire rack then turn it out to cool completely on the wire rack.
Meanwhile, trim the bottom of the Swiss chard stems, then slice the stems into 1/2-inch pieces. Cut the leaves into thin ribbons, about 1/4 to 1/2 inch wide.
Heat the olive oil in a large pot over medium high heat. Add the garlic and mushrooms and sauté for about 4 minutes until the mushrooms start to brown, and the garlic turns golden brown. Add the stems of the chard and sauté for another 2 minutes, season with salt and pepper then add the sliced leaves and continue to sauté for another 5 minutes until everything is wilted and tender. Add 1 tablespoon of vinegar, stir, taste and add more if desired. Let cool to room temperature.
Pile the chard and mushroom mixture onto the biscuit, and serve in wedges.
Notes
Use any variety of Swiss chard that you like, and any type of mushrooms. The vegetables get a little sharp tartness from a splash of vinegar, as much or as little as you like (also use any kind you have – no need to buy anything new for this!).