Add the mayonnaise, oil, mustard, Worcestershire and hot sauce to a small mixing bowl. Season with pepper then cover and refrigerate until ready to use, up to 1 week.

Add potatoes to a large pot, cover with salted water by 1” (2.5cm) and bring to a boil over medium-high heat. Cook the potatoes until they are tender, stirring occasionally, about 20 minutes. Drain the potatoes completely and add them back to the pot to help dry any remaining water. Rice the potatoes, add to a large mixing bowl and set aside.

Season the chicken with salt and pepper on both sides. Heat a large sauté pan over medium heat, add the olive oil and heat through. Add the chicken and cook until golden brown on both sides, about 6 to 8 minutes total.

Remove cooked chicken to a cutting board and let rest for 5 minutes, then finely dice the chicken and set aside.

Return the pan to medium heat, add the butter and allow to melt. Add the carrot, celery and shallots, sautéing until tender, about 6 minutes. Add the peas and garlic, continuing to cook until the peas are tender, about an additional 2 minutes.

Return the chicken to the pan, stirring to combine. Add the flour and stir to combine, cooking for just a minute so the flour flavor cooks off. Add the milk and stir, let simmer over medium low heat until the mixture thickens, about 5 minutes. Season with Worcestershire, salt and pepper.

Let cool, then add to the potatoes, stirring to combine, being careful not to over-mix.

Line a rimmed baking sheet with parchment paper. Scoop the filling in 2 tablespoon portions, shaping into balls and placing them on the baking sheet. Cover with plastic wrap and refrigerate until chilled, about 1 to 2 hours or up to overnight.

Add the eggs to one shallow bowl, whisking to combine. Add the breadcrumbs to another bowl.

Add enough oil to reach 1” (2.5cm) up the side of a large cast iron pan or Dutch oven. Heat oil to 350ºF (180ºC).

Working one at a time, roll one of the croquette balls in the breadcrumbs, then into the egg wash, and back into the breadcrumbs.

Carefully add to the oil and fry, working in batches so as not to overcrowd the pan, until golden brown on all sides, about 1½ to 2 minutes. Remove from the oil to a wire rack set over a rimmed baking sheet to drain.

Serve the croquettes on a platter with the sauce on the side for dipping.