Bring a pot of lightly salted water to a boil in a covered pot over high heat. Add the potatoes and cook for about 12-15 minutes, until soft when tested with a fork. Drain, then turn into a bowl. Add the butter, milk, and alittle sea salt and pepper. Mash well with a potato masher. Heat the olive oil in a medium-size skillet over medium heat. Add the shallots, alittle sea salt and pepper, and the thyme, and cook for about a minute, stirring frequently until softened and golden. Add the meatless chicken strips and the parsley and stir to coat with the oil. Cook for about 2 minutes until heated through. Turn the shallot-and-chicken mixture into a food processor fitted with a metal blade. Cover and process for about 20 seconds until finely minced. Turn this into the mashed potatoes. Stir well to combine. Taste for seasonings.
Scoop a 1-cup measure into your hand, then, using two hands, form into a rounded log-shaped croquette. Place this on a cookie sheet and continue forming the remaining mixture.
Crack the eggs into a shallow bowl. Add alittle sea salt and pepper; then, with a whisk or a fork, beat them until blended. Measure the bread crumbs into another shallow bowl. Using your hands, carefully dip one croquette into the beaten eggs, turning it to coat all sides. Then place the croquette into the bread crumbs and turn to coat. Place the breaded croquette back onto the cookie sheet and continue breading the remaining croquettes.
Heat the oil in a large skillet over medium-high heat. Add as many croquettes as you can fit in a single layer without crowding, leaving some space in between each croquette so that you can turn them. Cook for about a minute per side, using two slotted spatulas to turn until evenly browned but not burned. Transfer the browned croquettes to a platter and continue frying the remaining croquettes.