Preheat oven to 425 degrees F.
Place potatoes in a medium pot and cover with water. Season water with 1 teaspoon salt and bring to a boil over high heat. Reduce heat to medium and simmer for 5 minutes. Remove from heat and drain well.
Toss potatoes with 4 cloves sliced garlic, 4 sprigs of thyme, and 3 tablespoon olive oil. Season with salt and pepper. Spread in an even layer on a baking sheet and roast for 20 minutes, flipping the potatoes over halfway. Remove from heat and discard thyme sprigs.
Meanwhile, prepare the pickled onions. Microwave the vinegar for 45 seconds to 1 minute or until warm. Add sugar and salt and stir until dissolved. Pour mixture over the red onions and let sit for at least 5 minutes.
Prepare the lemon aioli. Combine 1 tablespoon lemon juice with 2 teaspoon horseradish and ¼ cup mayo in a small bowl. Season with salt and pepper.
Arrange the roasted potatoes on a platter and dollop the lemon aioli on top. Sprinkle pickled red onions, grated parmesan, and dill on top. Serve.