Rinse small red/new potatoes and carrots in colander.
Chop onion and mince garlic; combine in a bowl and set aside.
Scrape (remove outer layer) carrots, then chop carrots and potatoes into roughly same-size pieces. Combine in a separate bowl and set aside.
Cut roast into bite-sized pieces.
Combine flour, salt, and pepper in a shallow dish (i.e. pie plate).
Dredge the beef chunks thoroughly in the flour mixture.
Add enough oil to cover the bottom of your dutch oven or stockpot and preheat over medium to medium-high heat.
Thoroughly brown the beef chunks in the dutch oven or stockpot, in batches if necessary.
Remove browned beef, put in bowl or on a plate and set aside.
Sauté diced onion-garlic mixture in oil for around 4 minutes, being sure to scrape the browned bits (also called fond in some US recipes) from the bottom of the dutch oven or stockpot and incorporate.
Turn burner to simmer.
Add tomato paste, Worcestershire sauce, rosemary, and tarragon (or thyme), mix well and stirring constantly, cook for about 30 seconds to one minute to mix the flavors.
Add beef chunks, the bottle or can of Guinness, and enough beef bone broth to cover.
Cover pot, and simmer until beef is nearly done, adding more broth or water as needed. Depending on the size of your chunks, 1-1.5 hours.
Add chopped vegetables and continue to cook until they are tender and the beef is fork-tender.
Season to taste.
Serve with Irish soda bread or crusty bread, and a side such as colcannon or a simple salad.
And don't forget your pint of Guinness for drinking!