Saute the celery, carrots, onions, herbs, garlic, bay leaf, paprika and salt, pepper and sugar to taste (this is called a sofrito) in a medium saute pan, 5 to 7 minutes. Remove from the pan and cool until ready to use.
Pulse the shrimp in a food processor, leaving some larger shrimp pieces. Mix with the sofrito and sprinkle with salt.
Form the shrimp mixture into 4 to 6 burger patties. Sprinkle both sides of the burgers with salt and pepper.
Heat a large saute pan with the butter over medium-high heat. Cook the burgers until golden brown, about 3 minutes on each side. Pull the burgers from the pan and toast the buns in the butter (you may need to add a little more butter at this step, depending on how much is left in the pan).
To serve, top the burger with Aioli and Cabbage-Apple Slaw.
Place the egg yolks, lemon juice and hot sauce in a food processor and pulse to combine.
While the food processor is running, slowly add the oil to form an emulsion. Once the egg yolks and oil have emulsified, thin out with water (about 1/4 cup) and season with salt and pepper. Fold in the herbs. Store in an airtight container in the refrigerator for up to 1 week.
Mix together the cabbage and apples in a large bowl and season with salt.
Combine the lemon juice, olive oil and thyme in a small bowl. Season with salt, pepper and sugar. Mix the slaw with the dressing.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.