1. Preheat oven to 375 F. Season the duck breast with paprika, salt, and pepper.
2. Place the seasoned breast into a dry, cold pan. Place over a burner, set the flame to medium, and allow the pan and duck to heat up together for 6-8 minutes, until the fat is rendered and the skin is brown and crispy.
3. Flip onto flesh side for 1-2 minutes, then flip back to skin side. Transfer to oven and finish cooking until medium rare (internal temperature of 145 F, around 5-6 minutes. Allow to rest for 5 minutes before slicing.
1. In a small saucepan, simmer the sherry and vinegar until syrupy. Season with salt and pepper.
1. With a sharp knife, completely trim away all of the green parts (leaves and bases, choke, stem) of the artichokes, making sure to completely empty the inside. Cut the stems off completely so they will sit flat, forming cups.
2. Blanch the artichokes in boiling, salted water for 5-6 minutes. Remove them from the water, pat dry.
3. Heat enough oil in heavy pan to deep fry the artichokes (1-2 inches/2.5-5 cm).
4. When the oil reaches 350 F, fry the arugula for 8-10 seconds until it just crisps. Transfer immediately to a lined plate and season lightly with salt.
5. Add the artichoke cups to the hot oil and deep fry for 3-4minutes, until crispy. Remove from oil and season with salt.
1. Lay the slice of membrillo on left side of plate and meticulously shingle the thinly sliced olives in a nice pattern to fully cover it.
2. Slice the rested duck into 4 1-inch (2.5 cm) portions. To the right of the membrillo-olive garnish, at thefront of the plate, place a slice of the rested duck, skin side up, to reveal the doneness of the meat.
3. In the back right section of the plate, place the crispy artichoke cup, fill it with sherry reduction, and top it with crispy arugula.