Combine potatoes, thyme sprigs, and 2 tablespoons salt in a large saucepan.

Cover potatoes completely with cold water.

Bring to a boil over high heat.

Reduce heat to simmer and cook until potatoes are tender, about 10 minutes.

Drain the potatoes.

While hot, peel the potatoes with a sharp knife, protecting your hand.

Slice each potato crosswise into 1/4-inch slices and place into a mixing bowl.

Add onion, remaining salt, sugar, pepper, vinegar, and oil to the hot potato slices.

Gently stir until all ingredients are combined.

Heat broth in a large sauté pan over medium-high heat.

Add potato salad and stir gently until thoroughly heated.

Garnish with parsley or chives and serve immediately.