Warm the oil: Place the sauté pan over medium-low heat and add the olive oil. Let it warm gently — you want shimmer, not smoke.
Sweat the garlic: Add the thinly sliced garlic and sweat until fragrant and translucent, about 1–2 minutes. Don’t let it brown.
Bloom the paprika: Sprinkle in the smoked paprika and stir for 10–15 seconds to bloom the spice in the oil — this releases aroma and color.
Add tomatoes: Stir in the chopped (or canned) tomatoes, increase heat just to a gentle simmer, then lower again to keep a steady bubble.
Reduce to thicken: Let the sauce simmer, stirring occasionally, until it thickens and the flavors concentrate, about 10–15 minutes. Look for a jammy texture.
Finish and rest: Season with salt and pepper, add the lemon juice or sherry vinegar, fold in chopped parsley, remove from heat, and let rest 5 minutes to let flavors meld.
Serve: Use warm or at room temperature. Spoon over grilled fish, as a tapas bowl, or smear on hot toast with cheese.