Heat oil in large pot (or Dutch oven) over medium-high heat. Season beef. Brown meat on all sides, working in batches if necessary. Remove to plate.
Add onion to pot and reduce heat to low. Cook until softened, about 3-4 minutes. Add garlic and cook for about 1 minute.
Pour in root beer, broth, tomato paste, Worcestershire, paprika. 1/2 tsp kosher salt, pepper, and sugar (only if using beer). Return beef to pot. Simmer for 1 1/2 to 2 hours until meat is tender.
Stir in potatoes and carrots. Simmer until vegetables are tender and meat is falling apart, 30 to 45 minutes.
Remove 1 cup of liquid from pot and slowly whisk in flour. Slowly stir flour mixture back into pot and bring to a slow boil.
Reduce heat and simmer for 10 minutes until thickened. Adjust seasonings as needed. Garnish with fresh parsley.
If you want to make this in the crock pot, brown beef. Add beef and all other ingredients, except flour to crock pot. Cook on low for 10-12 hours, or on high for 4-6. Remove 1 cup of liquid and slowly add flour. Slowly stir four mixture back into crock pot. Cook on high for 15-20 minutes, or until thickened.