Step 1

Place 3 cups all-purpose flour and 3/4 cup instant mashed potato flakes in a medium bowl and whisk to combine.

Step 2

Place 1 cup whole milk and 4 tablespoons of the unsalted butter in a small saucepan. Heat over medium heat until the butter is melted and milk is just warm to the touch (110ºF and 115ºF). Pour into a large bowl. Sprinkle with 1 (1/4-ounce) packet active dry yeast and 3 tablespoons granulated sugar, and stir to combine. Let sit until foamy, about 5 minutes.

Step 3

Add 1 large egg and 1 1/2 teaspoons kosher salt and whisk to combine. Add the flour mixture and stir until a slightly shaggy dough forms.

Step 4

Lightly dust a work surface with all-purpose flour. Transfer the dough onto the surface and knead by hand until smooth and elastic, 4 to 5 minutes. Coat a large bowl with 1 teaspoon vegetable or canola oil. Transfer the dough to the bowl. Cover the bowl with plastic wrap. Let rise at room temperature until roughly doubled in bulk, about 1 1/2 hours.

Step 5

Melt 4 tablespoons of the unsalted butter in the microwave or on the stovetop. Lightly brush a 9x13-inch baking dish with some of the melted butter. Punch the down dough, then divide into 4 pieces (about 8 ounces each).

Step 6

Working with 1 piece at a time, roll out on a lightly floured surface into a 12x6-inch rectangle with a longer side closer to you. Cut lengthwise into 3 (2-inch wide) strips. Cut each strip crosswise into 3 (4x2-inch) rectangles. Brush each lightly with melted butter, then fold in half (butter on the inside) to create 2x2-inch squares.

Step 7

Place 1 dough square in the corner of the baking dish with the folded edge against the short side of the dish. Shingle the remaining rolls in a single row across the baking dish. Repeat with remaining dough to create 4 rows of 9 rolls. Brush with the remaining melted butter.

Step 8

Cover the baking dish in plastic wrap. Let rise at room temperature until the rolls have puffed, about 30 minutes. Meanwhile, arrange a rack in the middle of the oven and heat the oven to 350°F.

Step 9

Uncover and bake the rolls until golden and puffed, rotating the baking dish halfway, 25 to 35 minutes total. Melt the remaining 2 tablespoons unsalted butter in the microwave or on the stovetop. Brush over the rolls. Sprinkle with flaky salt. Serve warm with more butter if desired.