Bring a large pot of generously salted water to a boil. Add potatoes and cook until just slightly tender, 6 to 7 minutes; drain and set aside to let cool briefly. While still warm, grate potatoes on the large holes of a box grater and transfer to a large bowl. Using your hands, mix in chives, thyme, 1 1/2 tsp. salt, nutmeg, and pepper. Form mixture into 24 balls, using about 1 1/2 Tbsp. of the potato mixture for each. Press them together firmly so they hold their shape. (Clean your hands from time to time to make the shaping easier.) Place potato flakes in a medium bowl, then roll potato balls through flakes to coat, shaking off any excess; transfer to a sheet tray.
Pour oil into a large, deep skillet to a depth of 1/2 inch, then heat over medium-high heat; oil is ready when a potato ball sizzles vigorously when dropped in. Working in two or three batches, fry potato balls, turning occasionally, until deep golden brown, 6 to 8 minutes. Using a slotted spoon, transfer to a paper towel-lined sheet tray to let drain; serve warm.
Serve with sour cream or crème fraîche as an alternative to ketchup. They can be made a day in advance and reheated in the oven at 350° until hot and crispy.