Burrata: Pour flour, egg and panko into their own shallow dishes and set them up in that order. Dredge ball of burrata in flour, dusting off any excess. Next dredge the ball in the beaten egg followed by the panko. Dredge ball back into the beaten egg, then back into the panko for a double coating. Place ball on a small, parchment lined plate and place in freezer for 10-15 minutes.
Romesco Sauce: Place all ingredients into a food processor or blender, season with salt and pepper and blend until smooth. Pour mixture into a saucepan and simmer until warm or hot, 5 to 7 minutes.
Fill a tall saucepan with about 4 inches oil and heat to 350˚F.
Carefully fry burrata in oil for 3 to 4 minutes or until golden brown. Remove from oil and transfer to a paper towel lined plate. Lightly season with salt and pepper.
Assemble: Pour romesco sauce into a shallow bowl and place fried burrata into center or sauce. Top with fresh basil leaves and serve with toasted crostini.