In a large bowl, toss beef cubes with flour, salt, and pepper.
Warm 1/3 of the oil in a large Dutch oven or heavy pot on medium-high heat. Add meat in a single layer without crowding. Brown on all sides, about 5 to 7 minutes. Remove beef; transfer to a bowl. Repeat with remaining meat.
Add 1/4 cup of the broth to deglaze the pot, stirring with a wooden spoon, scraping loose any browned bits on the bottom of the pot. Transfer cooking liquid to bowl with meat.
Add the remaining oil to the pot over medium-low heat. Add onion and cook 5 minutes, stirring. Return reserved beef and juices to the pan. Add remaining broth, tomatoes, and thyme. (Add more broth if needed, to cover.) Increase heat and bring to a boil. Reduce heat to medium-low, cover, and simmer for 30 minutes.
Add carrots and potatoes to the pot. Let simmer, covered, for 45 minutes or longer if needed until the beef is very tender and vegetables are cooked through. Stir in the peas and parsley.
Toast the bread. Then spread with butter.
Portion the beef stew; serve with bread and sparkling water.