Preheat your oven to 400°F (200°C) and line a large sheet pan with parchment paper.
Dice the potatoes into 1/2-inch cubes and slice the carrots into thin rounds.
Toss the potatoes and carrots on the baking sheet with olive oil, half of the sea salt, and half of the black pepper.
Spread the vegetables in a single layer and roast for 15 minutes.
While the vegetables are roasting, whisk together the Greek yogurt, Dijon mustard, parsley, dill, garlic powder, and the remaining salt and pepper in a small bowl.
Remove the sheet pan from the oven, add the sliced zucchini, and move the vegetables to the sides to create space in the center.
Place the salmon fillet in the center of the pan and spread the herb-yogurt mixture evenly over the top of the fish.
Return the pan to the oven and roast for an additional 12 to 15 minutes, or until the salmon is opaque and flakes easily with a fork and the vegetables are golden brown.