How to Make It
Roast the eggplant directly over a gas flame, turning occasionally, until charred all over and soft, about 12 minutes. Transfer to a colander and let cool slightly, then peel and let cool completely.
Meanwhile, in a medium saucepan, cook the garlic in the oil over moderate heat until sizzling, about 2 minutes. Remove from the heat and whisk in the vinegar, honey, rosemary, oregano and minced parsley. Season the vinaigrette generously with salt and pepper.
Heat a large cast-iron skillet. In batches if necessary, add the piquillos to the skillet in an even layer. Cook over high heat, turning once, until lightly charred on both sides, about 2 minutes total. Add the piquillos to the warm vinaigrette and let cool completely.
In a food processor, combine the eggplant with both cheeses and puree until smooth. Scrape into a bowl and season with salt and pepper. Spread the whipped eggplant on toasts and, using a slotted spoon, spoon some of the marinated piquillos on top. Garnish with chopped parsley and serve with anchovies.