Step 1

Peel the potatoes, then cut them into rough 1 ½-inch chunks. Place the potatoes in a large saucepan and cover by at least 1 inch with cold water. Season the water liberally with kosher salt, then place the pot over high heat and bring to a boil. Once the water starts boiling, continue cooking the potatoes, stirring occasionally, until half-cooked — you should be able to just pierce the largest pieces halfway through to their middles with the tines of a fork without the pieces breaking apart — about 5 to 15 minutes, depending on how big the pieces are and how long your stove takes to heat your pot of water.

Step 2

Drain the potatoes in a colander in the sink, then transfer them back to the pot. Clamp on the lid and, with mitts or folded kitchen towels on your hands for protection, give the whole pot 3 to 4 shakes to rough up the potatoes. Spread the potatoes out on a parchment paper-lined baking sheet and let cool completely to room temperature. Wrap in plastic wrap and store in the refrigerator until ready to use, up to 2 days.

Step 3

Meanwhile, make the Caesar sour cream: Finely mince the anchovies on a cutting board, then sprinkle with the kosher salt. Use the flat side of your knife to scrape the salt into the anchovies repeatedly until you form a smooth paste; scrape the paste into a bowl. If using anchovy paste, simply stir it and the salt together in a bowl. Using a microplane, grate the garlic into the bowl. Stir in the lemon juice, Worcestershire sauce and red wine vinegar, then let stand for 5 minutes.

Step 4

Stir in the sour cream, mayonnaise and all but 1 tablespoon of the Parmesan. Season with lots of black pepper and more salt, if needed. Transfer to a serving bowl, sprinkle with the remaining Parmesan and more black pepper and cover with plastic wrap. Refrigerate until ready to serve. This makes just shy of 2 cups.

Step 5

When ready to cook the potatoes, pour the fat into a large roasting pan and set the roasting pan in the oven. Heat the oven to 500 degrees so the pan and fat can get blazingly hot, at least 10 minutes.

Step 6

While the oven heats up, arrange the cucumber, celery and fennel wedges on a large serving platter. Place the bowl of Caesar sour cream on the platter with the veggies and drape a sheet of plastic wrap or lightly moistened paper towel over the vegetables to keep them from drying out. Refrigerate the platter until ready to serve.

Step 7

Using caution, open the oven and pull the hot roasting pan out of the oven, then use the parchment paper to carefully topple the cold potatoes into the hot fat. Give the pan a shake to disperse and settle the potatoes evenly, then return the pan to the oven and let the potatoes roast for 20 minutes. Using a slotted spoon, flip the potatoes in the fat, and continue roasting until deep golden brown and intensely crunchy, 25 to 30 minutes more.

Step 8

Using the slotted spoon, transfer the potatoes out of the fat and onto paper towels to drain for 1 minute. Season with flaky salt while hot, then transfer to a serving bowl or plate. Serve immediately alongside the cold platter of crudité and Caesar sour cream.