Heat a pot over medium heat (or use the sauté function on a slow cooker if available).
Once hot, add the olive oil. Sauté the onion, celery, carrots, and garlic until softened, about 3–5 minutes. Add the beef to the pot, browning it well. Then add to a slow cooker.
Pour in the beef broth and canned diced tomatoes. Add the diced potatoes and fresh thyme sprigs. Season with salt and pepper. Set the slow cooker on low for 5 - 8 hours or high 2 - 4 hours.
Make the soda bread: Preheat oven to 375F (190C). Line a baking sheet with parchment paper.
In a large bowl, mix together flour, sugar, baking soda, baking powder, salt and softened butter. Stir in buttermilk and egg, mix until combined. Turn dough out onto a lightly floured surface and knead slightly. Form dough into a round and place on prepared baking sheet. Use a sharp knife to cut an 'X' into the top of the loaf.
Bake in preheated oven until a toothpick inserted into the center of the loaf comes out clean, 30 to 40 minutes. Check for doneness after 30 minutes.Intermittently through baking brush the loaf with melted butter to get a nice golden brown on top. Let cool before slicing.
Prior to serving the stew stir in the green beans and let cook for another 15 minutes.
Remove the thyme sprigs.
Ladle the stew into bowls, serve with soda bread and beer.