Sear Zucchini: Heat the skillet over medium-high heat. Add half of the olive oil and let it shimmer. Place half the zucchini slices in a single layer and cook until deep golden brown on one side (about 4 minutes). Sprinkle with ¼ teaspoon salt, then flip and brown the other side (about 4 minutes more). Remove and set aside on paper towels. Repeat with remaining oil, zucchini, and salt.
¼ cup olive oil, 3 medium zucchini, ½ teaspoon kosher salt
Add Parmesan: Transfer all browned zucchini to a serving platter and sprinkle evenly with Parmesan while still warm so it melts slightly.
¼ cup freshly grated Parmesan cheese
Make Vinaigrette Base: Pour off all but 1 tablespoon of oil from the skillet. Add anchovy paste (or chopped anchovies) and mash with a wooden spoon until dissolved and fragrant.
2 teaspoons anchovy paste
Add Flavorings: Stir in capers, oregano, red pepper flakes, and diced tomato. Squeeze in lemon juice and stir until everything is combined and aromatic.
2 tablespoons capers, ¼ teaspoon dried oregano, ¼ teaspoon red pepper flakes, 1 medium vine-ripened tomato, 1 tablespoon fresh lemon juice
Finish & Serve: Spoon the tomato-anchovy vinaigrette over the zucchini. Sprinkle with parsley. Serve warm or at room temperature.
2 tablespoons chopped fresh Italian parsley