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Step 1
Pour the ranch dressing mixture into a small, half-round ice cube tray, filling 18 of the molds. Use an offset spatula to scrape away any excess so the dressing is flush with the top edges of each mold. Transfer to the freezer until the ranch is frozen solid, at least 2 hours, or preferably overnight.
Step 2
Cook the potato shreds according to the package instructions. Let cool while you make the sauce.
Step 3
Make the béchamel sauce: In a small saucepan over medium heat, melt the butter until it begins foaming. Add the flour and whisk to form a paste. Reduce the heat to medium and cook, whisking constantly, until the raw flour smell is gone but the flour has not browned, about 1 minute.
Step 4
While whisking constantly, slowly pour in the milk until incorporated. Continue to cook, stirring often, until the béchamel is thick enough to coat the back of a spoon, about 2 minutes. Season with salt, pepper, and nutmeg to taste. Let cool for 10 minutes.
Step 5
Add the potatoes to a large bowl with the béchamel sauce and use a rubber spatula to mix until evenly combined. Season with more salt, pepper, and/or nutmeg to taste, if needed.
Step 6
Assemble the croquettes: Line a quarter-sheet pan with parchment paper.
Step 7
Using a 2½-tablespoon cookie scoop or measuring spoon, scoop the potato mixture onto the prepared baking sheet; you should have 9 portions. Chill in the fridge until the potato balls are firm, about 1 hour.
Step 8
Remove the ranch ice cubes from the freezer, unmold, and press the halves together to make 9 balls.
Step 9
Remove the potato mixture from the freezer. Flatten one portion in your hand and place a ranch ball in the center. Wrap the potato mixture around the ranch ball to encase completely, then roll the potato mixture into a ball. Return to the baking sheet and repeat with the remaining potatoes and ranch balls. Cover loosely with plastic wrap and refrigerate until thoroughly chilled, about 1 hour. .
Step 10
Add the flour to a shallow bowl. Beat the eggs in a second shallow bowl. Process the panko bread crumbs in a food processor until finely ground, then transfer to a third shallow bowl.
Step 11
Roll each potato ball in the flour, then coat in the eggs, then roll in the bread crumbs to coat completely. Return to the prepared baking sheet and freeze while you heat the oil.
Step 12
Add the vegetable oil to a Dutch oven and heat over medium-high heat until the temperature reaches 350°F (180°C). Carefully add 3 croquettes at a time to hot oil using a spider or slotted spoon and fry, turning occasionally, until golden brown on all sides, about 90 seconds. Transfer the croquettes to a wire rack and season with salt. Let the oil return to 350°F (180°C) between batches.
Step 13
Serve immediately.
Step 14
Enjoy!