Brown the oxtails: Pat dry oxtails with paper towels.
Sprinkle oxtails all over with salt and pepper.
Heat 1 tablespoon of vegetable oil on medium to medium high heat
Using a slotted spoon, transfer the beef to a plate.
Repeat with the remaining beef. Discard the oil and wipe out the pan.
Return the pot to the stove and melt the butter over medium high heat.
Add the onion and cook, stirring, until lightly browned, about 5 minutes.
Add the garlic and cook, stirring, until fragrant, about 1 minute.
Add the tomato paste and cook, stirring, until lightly browned, about 1 minute more.
Add the carrot, and celery, potato to the pan. Cover, and cook on Low setting for 4 to 6 hours.