Set a rack in the top third of the oven and heat the oven to 450 degrees F.

Put the tomato, almonds, roasted red pepper, garlic, cayenne, 1/4 teaspoon salt, and a few grinds of black pepper in a food processor. Process, scraping the bowl as needed, until the mixture is somewhat smooth, about 1 minute. Add the vinegar and 1 tablespoon of the olive oil and process until well incorporated. Taste and add more salt if needed.

Trim the ends off of each potato and cut the potatoes crosswise into 1/8- to 1/4-inch slices. In a bowl, toss the potatoes with the remaining 3 tablespoons olive oil and 1 teaspoon salt to coat well. Lay the slices in a single layer on a baking sheet. Roast the potatoes, turning the slices with a spatula and rotating the baking sheet halfway through roasting, until golden brown, 20 to 30 minutes. Let the potatoes cool slightly.

To serve, arrange the potato slices on a serving platter; blot with a paper towel if they look oily. Top each slice with a generous 1/4 teaspoon of the romesco sauce (you may not use all the sauce). Garnish each hors d'oeuvre with a tiny pinch of lemon zest and a parsley leaf.

The sauce can be made up to three days ahead and refrigerated. Before using, bring it to room temperature and stir well.