Heat a saute pan over high heat. Lightly coat the bottom with olive oil. When the oil begins to shimmer, add the artichoke slices, reduce the heat to medium-low, and saute the artichokes until they're tender, about 10 minutes, stirring occasionally. Season the artichokes with salt as you saute them. Remove them from the heat.
Crack the eggs into a medium bowl. Add the egg whites and season them with a few pinches of salt. Whisk them until they're well blended.
For a large frittata, heat a large nonstick pan over medium-high heat and then add 1/2 tablespoon of butter and allow it to coat the bottom of the pan. Place half of the cooked artichoke slices in the pan and sprinkle them with parsley and thyme. Reduce the heat to low and pour half of the egg mixture over the artichokes.
Quickly stir everything together so that the artichokes are evenly distributed. Cook the mixture, without stirring, until the eggs are almost set, approximately 4 minutes, and then flip the frittata over and let it cook for another minute or so. Slide out of the pan and onto a serving plate.
Repeat step 4 to make a second frittata. Cut each frittata into 3 pieces. Serve hot or cold with bread.