Heat a large stock pot over medium heat and add the oil. Toss the beef piece with a sprinkle of salt and pepper, then toss them with the flour so all the pieces are coated.
Add the beef to the pot and sear until each side is golden brown, about 1 to 2 minutes per side. You may need to do this in batches. Remove the beef pieces with a slotted spoon and place them on a plate until ready to use.
To the same pot, toss in the butter, onions and garlic. Stir and toss, scraping the bottom so you remove some of the brown bits of flavor from the beef. Cook for 5 minutes, until softened.
Stir in the potatoes and carrots with a pinch of salt and pepper. Cook for another 5 minutes. Stir in the tomato paste and make sure all the pieces are coated. Cook for another 5 to 10 minutes to develop the flavor, stirring often so the tomato paste doesn’t burn on the bottom. Add the beef back to the pot.
Pour in the stout to deglaze the pan. Stir to release any more bits of flavor from the bottom. Stir in the beef stock. Add a sprig of thyme or rosemary to the pot. Bring the mixture to a boil, then reduce it to a simmer. Cover and cook for 30 to 60 minutes, until the beef is tender and falling apart. You can simmer it for even longer as long as it’s covered! I like to taste it here and see if it needs any additional salt and pepper. If so, add it!
To make the dumplings, whisk together the flour, baking powder, herbs and salt in a large bowl. Combine the milk and the eggs, then stir into the flour until just mixed. Set the mixture aside for 10 minutes.
Once the beef is tender, uncover the soup and add spoonfuls of the dumpling dough directly to the broth. I don’t worry about crowding the pot and usually cover the entire top of the stew mixture. You want the mixture to be bubbling for 10 to 15 minutes so it cooks the dumplings – after 10 minutes I usually gently flip the dumplings over and cook for another 5 to 10 minutes.
Serve the stew immediately with chopped parsley or rosemary, or both!