Place the potatoes in a large saucepan and cover with cold water. Add a large pinch of salt and bring to a boil, Reduce to a simmer and cook until fork-tender, about 10-15 minutes depending on the size of the potatoes. Larger potatoes may take longer. Remove the potatoes from the water and set aside until cooled, about 30 minutes. Rinse or place in cold water to speed along the process.
Spread a layer of the salted butter over each slice of rye bread.
Peel the boiled potatoes if desired and slice about 1/4 inch thick. Arrange in an overlapping layer over the buttered bread.
Top with a line of mayonnaise, followed by a sprinkling of the raw and fried onions. Top with the chives and place 1 sprig of thyme over each.
Sprinkle each smørrebrød with a pinch of salt and black pepper. Serve immediately.