The unique thing about these potatoes is that they pool together and stretch like taffy when you fork a bite. Cook's Illustrated explains that the signature texture is achieved by releasing amylose, a type of starch, through food processing and extended stirring. Apparently they have a whole festival in Southern France dedicated to these potatoes! And after making them myself, I now know why.
French Mashed Potatoes with Cheese and Garlic (Aligot)
From Cook's Illustrated
2 lbs. Yukon Gold potatoes (4 to 6 medium), peeled, cut into 1/2-inch-slices, rinsed well, and drained
Table salt
6 T. unsalted butter
1-1 1/2 c. whole milk
2 medium garlic cloves, minced
4 oz. mozzarella cheese, shredded
4 oz. Gruyere cheese, shredded
Ground black pepper
Place potatoes in a large saucepan; add water to cover by 1" and add 1 T. salt. Partially cover pan with a lid and bring to a boil over high heat. Reduce heat to medium-low and simmer until potatoes are tender and break apart when forked. Drain potatoes and dry saucepan.
Transfer potatoes to a food processor; add butter, garlic, and 1 1/2 t. salt. Pulse until butter is melted and incorporated into potatoes. Add 1 c. milk and continue to process until potatoes are smooth and creamy, about 20 seconds, scraping down sides halfway through.
Return potato mixture to saucepan and set over medium heat. Stir in cheeses, 1 cup at a time, until incorporated. Continue to cook potatoes, stirring vigorously, until cheese is fully melted and mixture is smooth and elastic, 3 to 5 minutes. If mixture is difficult to stir and seems thick, stir in 2 T. milk at a time ( up to 1/2 cup) until are potatoes are loose and creamy. Season with salt and pepper. Serve immediately.