Preheat the oven to 450°F (230°C). Line a baking sheet with foil or parchment if desired.
Toss the potato chunks with 2 tablespoons melted butter and a generous pinch of salt and pepper on the prepared baking sheet so they are in a single layer.
Roast the potatoes for 15 minutes, until they begin to soften and brown.
While the potatoes roast, make the Dijon dressing: whisk together the grainy Dijon, smooth Dijon, lemon juice, chopped shallot, chopped thyme, cayenne, salt, pepper, and the remaining 4 tablespoons melted butter until combined.
Remove the baking sheet from the oven. Toss the partially roasted potatoes with the panko, sesame seeds, and chopped garlic to coat evenly.
Place the salmon fillets on the baking sheet among the potatoes. Spoon half of the Dijon dressing over the salmon fillets.
Bake for about 10 minutes, until the salmon reaches your desired doneness (cook time may vary by thickness).
In the last 1 minute, switch the oven to broil and broil briefly until the tops are lightly charred; watch closely to avoid burning.
Meanwhile, toss the arugula or shaved asparagus with the chopped dill and 1–2 tablespoons of the remaining Dijon dressing; season with salt and pepper to taste.
Remove the salmon and potatoes from the oven. Spoon the remaining dressing over the salmon, then serve the salmon and potatoes topped with the dressed greens.