Crack the eggs into a large bowl and mix in salt. Spoon out half the jar of pisto, making sure to leave behind excess oil, and add to the eggs. Stir until combined.
Heat 2 tablespoons of the oil in a small sauté pan over a medium flame. When the pan is hot, add the egg mixture and stir briskly a few times with a wooden spoon to prevent the eggs from sticking. Shake the pan in a circular motion for 10 seconds to keep the mixture loose as the eggs start to cook. Lower the temperature and cook for one minute more.
Place a plate over the pan and invert the pan and plate together so the tortilla winds up on the plate, raw side down. If the pan looks dry, add the remaining 2 tablespoons of olive oil. Return the tortilla to the pan by sliding it back in, raw side down. Cook for another 60 seconds, until the bottom has fully set. To us, the perfect tortilla is very creamy and slightly runny in the middle.
Slide the finished tortilla onto a serving plate and garnish with a few basil leaves or sprigs of thyme and serve. Tortilla can be served warm, room temperature, or cold – just be sure to garnish right before serving.