Step 1

Pulse membrillo, vinegar, Aleppo-style pepper, and lemon juice in a food processor until smooth. Transfer to a small bowl.

Step 2

Do Ahead: Spiced membrillo can be made 1 day ahead. Cover and chill.

Step 3

Using floured hands, form a heaping tablespoonful of goat cheese into a 1½"-long log. Transfer to a parchment-lined baking sheet. Repeat with remaining cheese to make 15 more logs. Chill until firm, about 20 minutes.

Step 4

Pulse panko in a food processor until very finely ground; transfer to a shallow bowl. Whisk eggs and 1 Tbsp. cold water in a second shallow bowl. Place remaining 1 cup flour in a third shallow bowl. Dredge a log of goat cheese in flour, shaking off excess. Dip in egg mixture, letting excess drip back into bowl, then coat in panko, pressing to adhere. Repeat process to create a second coating. Transfer to a baking sheet. Repeat with remaining logs of goat cheese. Chill croquettes in freezer until firm but not frozen solid, about 15 minutes.

Step 5

Pour oil into a large heavy pot to come 2" up sides. Fit pot with thermometer and heat oil over medium-high until thermometer registers 350°. Working in several batches to avoid crowding the pan, fry croquettes, turning occasionally, until golden and crisp, about 2 minutes. Transfer to paper towels to drain; season with salt.

Step 6

Serve croquettes with spiced membrillo.