Heat a pressure cooker over medium-high heat until hot. Add the oil then add the beef in a single layer. If they don't all fit in a single layer you may have to brown it in batches. Fry one side until a brown crust forms and then flip them over and brown the other side.
Transfer the browned beef to a bowl and set aside.
Add the onions, bell peppers, carrots, garlic and sugar to the pot and use the liquid released to scrape up the browned beef juices off the bottom of the pan.
Turn down the heat to medium and sautée the vegetables, stirring regularly until the onions are soft and the whole mixture is a medium brown color (10-15) minutes.
Return the meat and any collected juices to the pan. Add the canned tomatoes and crush them up. Fill the can with water and add the water to the pan. Then add the tomato paste, vinegar, thyme, salt, pepper, chili powder, and ground cumin.
Seal the pressure cooker lid and set to high pressure. Bring the pot up to pressure over high heat (it will start whistling), and then turn down the heat enough so it barely maintains a constant whistle. Cook for 30 minutes and turn off the heat, allowing the pressure to drop naturally before opening the lid.
If you're not using a pressure cooker, just simmer the mixture for 1 1/2 hours, or until the meat is fall apart tender.
Once the beef is tender, skim off as much excess fat as you can. Use a potato masher to shred the beef. If there's still too much liquid, simmer the mixture uncovered until it's the right consistency.
When the sloppy joe mixture is done, taste it and adjust the salt, sugar and vinegar until you're happy with the taste. Serve hot in a hamburger or hotdog bun.