For the beef: Using paper towels, pat-dry the stew meat. Salt and pepper in all sides and set aside. Heat one tablespoon of olive oil in a large heavy bottom pot in medium-high heat. Once it is sizzling hot, add in half of the seasoned beef and cook for 3 minutes on each side. (The beef will not fully be cooked)Transfer to a plate. Repeat the same steps with the rest of the olive oil and meat. Transfer the second batch to the plate and cover it with aluminum foil. Do not wash the pot. To make the soup: Heat olive oil in the now-empty pan in medium-high heat. Add in onion, carrots, and celery. Using a wooden spoon, cook the vegetables, scraping the bits and pieces of meat at the bottom of the pan, until they are translucent, 8-10 minutes.
Stir in the garlic and cook for 30 seconds.
Add in the tomatoes, potatoes, thyme, and bay leaf. Give it a stir.
Transfer the semi-cooked beef into the pot. Pour the stock and water over everything, sprinkle it with salt and pepper, and give it a stir.
Turn down the heat to medium, put the lid on, bring it to a boil and then let it simmer for 15 minutes.
Add in the green beans and frozen peas and cook until green beans are cooked, but still firm, for 10-15 minutes more. Fish out the bay leaf.
When ready to serve, ladle into bowls and garnish with fresh parsley.