Heat olive oil in stock pot over medium heat; sear roast in the hot oil until slightly browned, about 2 minutes per side. Remove roast from pot and place on a plate. Cook and stir onion and garlic in the hot oil until onion is lightly browned, 10 to 15 minutes.
Return seared roast to the stock pot; pour coffee and 1 1/2 cup water over roast. Add beef bouillon, basil leaves, 1 tablespoon salt, and pepper.
Bring broth to a boil; reduce heat to medium low, cover stock pot, and simmer until meat is falling apart, 2 to 3 hours. Remove and discard basil leaves. Transfer roast to a serving dish and cover with a lid or aluminum foil, keeping the broth in the stock pot over medium heat.
Whisk flour and 1/2 cup water together in a bowl until smooth. Slowly whisk flour mixture into broth until gravy is smooth and somewhat clear; season with salt. Pour about half the gravy over the roast and pour the rest into a gravy boat for serving.