Preheat oven to 300 degrees F.
In a large bowl combine the lime juice, cumin, onion powder, garlic powder, salt and pepper. Stir to combine. Add the beef and stir to coat.
In a large skillet set over high heat, add the olive oil and heat for about a minute. Add the beef and brown for about 3-4 minutes.
Remove meat from stove top and put it in an oven proof dish. Pour over beef stock. Put it in the oven oven uncovered for about 3 1/2 hours or until really tender. NOTE: You will add the peppers to the beef about 45 minutes before it's finished cooking. You will see this below.
In the reserved skillet set over high heat, add the peppers. Give them a good stir and cook them for about 5 minutes or until they start to soften. Remove from heat.
After the beef has been cooking for about 2 hours and 45 minutes remove it from the oven and add the peppers. Stir well, cover and return to oven for remaining 45 minutes.
When beef is tender, remove from oven.
Add the cornflour to a glass and add the water. Stir to combine.
Using two forks, start pulling apart the beef till it flakes apart. Pour the beef into a large saucepan set over medium heat. When it starts to simmer, pour in cornflour mixture and stir until sauce thickens. Remove from heat.
Serve in tortilla wraps topped with cheese and arugula (if desired).