Trim the stems of the artichokes so they are flush with the bottom of the globe. Slice off the leaf tips and peel the leaves until the light yellowish-green leaves are revealed. Slice the globes thinly. As you slice them, place them into cold water containing just a few drops of lemon juice. This will help them to retain their color.
When they are all sliced, drain them and sauté in 2 tablespoons of olive oil in a large skillet.
Continue cooking for about 10 minutes, or until tender. Set aside.
Cook the bacon in an ovenproof skillet until crisp and golden brown. Remove the bacon with a slotted spoon and drain on a paper towel. Set aside.
Add the remaining olive oil to the skillet and cook the potatoes over medium heat, covered, for approximately 10 minutes.
Turn the potatoes, add the bacon, artichokes, and garlic. Cover and cook for 10 more minutes.
Turn again, crushing the potatoes. Cover and cook for an additional 20 minutes, or until the potatoes are tender.
Add garlic during the last 20 minutes of cooking. Season with salt and pepper.
Preheat the oven to 500 F.
Turn the mixture again, continuing to crush the potatoes. Sprinkle the cheese over the top and let it melt.
Put the skillet into the oven for about 5 minutes, or until the cheese browns.