Heat oil in a large skillet over medium heat until shimmering. Sprinkle the beef on all sides generously with Kosher salt and pepper, then add them to the pan. Brown for 2-3 minutes, or until the beef releases easily. Flip and brown the other side. Add a splash of the wine and deglaze the pan. Transfer the beef and any browned bits from the pan into the slow cooker.
In the slow cooker, stir together the beef, carrots, onions, mushrooms, diced tomatoes, garlic, red wine, broth, and seasonings. Cover and cook on low for 8 hours or on high for 4 hours.
When the slow cooker is almost finished, start the dumplings. Whisk together the flour, baking powder, salt, and sugar in a medium bowl. Add the chunks of butter and use your fingers or a pastry cutter to work the butter into the flour mixture, until small pea-sized pieces are distributed evenly throughout it. Pour the milk in and gently stir together until a shaggy dough forms. If there are any very dry spots (pockets of completely dry flour), add additional milk, a teaspoon at a time, until it comes together.
Uncover the stew mixture and drop heaping Tablespoon sized balls of dumpling dough onto the stew pieces. Try to drop it on the veggies and meat pieces rather than directly into the liquid. Cover and allow dumplings to cook for 25-30 minutes or until puffed and toothpick inserted in center comes out clean.
Sprinkle with parsley if desired, and serve each individual bowl with a dumpling portion.