Step 1Heat 1 1/2 tablespoons oil in 10-inch heavy-bottomed skillet over low heat. Add potato slices, making sure they don't stick and clump together. Cook until softened, stirring frequently, 8 minutes. (Potato slices shouldn't turn brown, but don't worry if a few do.) Add green and red peppers, thyme and salt and pepper to taste and cook until tender, stirring frequently, 8 minutes.
Step 2Whisk eggs with salt and pepper to taste in large bowl. Remove potatoes and peppers from skillet with slotted spoon, keeping excess oil in skillet. Add vegetables to whisked eggs; let sit 3 minutes.
Step 3Heat 1 tablespoon oil in skillet over medium heat. There should be enough to coat bottom of pan; add another 1/2 tablespoon oil if necessary. Add eggs and vegetables, and spread across bottom of skillet. Cook until bottom of tortilla is set and golden brown, about 3 minutes. (Top will still be wet.)
Step 4Broil 4 inches from heat source until almost set on top, 1 to 2 minutes. Tortilla should still be slightly moist, but not wet. Use spatula to loosen bottom from skillet. Place plate on top of skillet and invert tortilla onto plate. Sprinkle with parsley before serving. Cut into wedges and serve warm or at room temperature.