Heat oil in a stock pot over medium heat. Sear roast in hot oil until slightly browned, about 2 minutes per side. Transfer roast to a plate.
Add onion and garlic to the pot; cook and stir until onion is lightly browned, 10 to 15 minutes.
Return roast to the pot; pour coffee and 1 ½ cup water over top. Add bouillon, basil, salt, and pepper; bring to a boil. Reduce the heat to medium-low, cover, and simmer until meat is falling apart, 2 to 3 hours.
Transfer roast to a serving dish and cover with a lid or aluminum foil. Discard basil leaves. Keep broth in the pot over medium heat.
Whisk flour and remaining ½ cup water together in a bowl until smooth; slowly whisk into broth until gravy is smooth and somewhat clear. Taste and adjust salt as needed.
Pour about ½ of the gravy over roast, and pour the rest into a gravy boat for serving.
