Preheat your oven to 400°F and line a small baking sheet with parchment paper.
Toss the cubed sweet potatoes with 0.5 teaspoon of olive oil and a pinch of sea salt, then spread them evenly on the baking sheet.
Roast the sweet potatoes for 20-25 minutes until they are golden and tender when pierced with a fork.
While the potatoes roast, season the lamb rack on all sides with the sea salt and black pepper.
Heat the remaining 1 teaspoon of olive oil in a heavy, oven-safe skillet over medium-high heat.
Sear the lamb rack for 2-3 minutes per side until a deep golden-brown crust forms.
In a small bowl, combine the finely chopped rosemary, thyme, and minced garlic.
Brush the fat side of the lamb with Dijon mustard and press the herb and garlic mixture firmly into the mustard to coat.
Place the skillet in the oven and roast for 12-15 minutes, or until the internal temperature reaches 135°F for medium-rare.
Transfer the lamb to a cutting board and let it rest for 10 minutes to allow the juices to redistribute before slicing between the bones.