Pat dry the drained hearts of palm with a clean kitchen towel.
Cut the hearts of palm into 3/4 to 1-inch long pieces on a cutting board.
Prepare a breading station: 2 Tablespoons of flour on one plate, 1 Tablespoon of flour mixed with non-dairy milk in a bowl, and 1/4 cup panko breadcrumbs with 1/2 teaspoon Old Bay seasoning on another plate.
Bread each heart of palm piece by rolling in flour, then dipping in milk mixture, and finally coating in seasoned panko breadcrumbs. Set aside on a clean plate.
Heat about a half inch of avocado oil in a non-stick skillet over medium-high heat until a dropped breadcrumb bubbles immediately.
Fry the breaded hearts of palm in batches for about 4 minutes, rotating until golden brown on all sides. Adjust heat as needed for subsequent batches.
Once browned, transfer the fried hearts of palm to a clean, towel-lined plate to drain excess oil.
Shake more Old Bay seasoning over the hot 'shrimp' and serve immediately with cocktail sauce for dipping.
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