Preheat your oven to 400°F (the original recipe calls for 350°F, but I find the higher heat creates better caramelization and crispy edges on the potatoes). Cut the potatoes into 1-inch cubes for even roasting. In a large bowl, toss the potato cubes with butter, olive oil, minced garlic, salt, pepper, and smoked paprika until evenly coated. Spread them in a single layer on a large rimmed baking sheet and roast for 30-35 minutes, stirring halfway through, until the potatoes are golden brown and tender when pierced with a fork.
While the potatoes roast, prepare the dressing. In a jar with a tight-fitting lid, combine both mustards, honey, apple cider vinegar, and fresh lemon juice. Seal the jar and shake vigorously for about 30 seconds until the dressing emulsifies and becomes creamy and well-blended. I prefer using a combination of smooth and whole grain mustard because the whole grain adds visual texture and a pleasant pop when you bite into it, while the creamy mustard creates a silky base.
Remove the roasted potatoes from the oven and transfer them to a large bowl while they're still warm. This is important—the warm potatoes will absorb the dressing better and allow the flavors to meld together more effectively. Add the finely diced red onion and fresh thyme to the warm potatoes, then pour the honey mustard dressing over everything. Gently toss until all the potatoes are evenly coated with the dressing. Taste and adjust seasoning if needed.
Let the potato salad rest for 5 minutes to allow the flavors to fully develop and meld together. Serve warm or at room temperature, depending on your preference. I like to serve this while it's still slightly warm because the dressing clings to the potatoes better and the overall dish feels more cohesive.