Preheat the oven: Preheat your oven to 400°F (200°C). Line a large baking sheet with parchment paper or lightly grease it.
Prepare the glaze: In a small bowl, whisk together Dijon mustard, whole grain mustard, honey, garlic, olive oil, lemon juice, apple cider vinegar, and smoked paprika until smooth. Set aside.
Prepare the vegetables: Toss carrots with 1 tbsp olive oil, salt, and pepper. Spread them on one side of the baking sheet. Roast for 10 minutes first, as they take longer to cook than the salmon and green beans.
Add salmon and green beans: After the carrots have roasted, remove the sheet pan from the oven. Push the carrots to one side and add the salmon fillets (skin side down, if using). Brush the honey mustard glaze generously over each fillet. Toss the green beans with the remaining olive oil, salt, and pepper, and spread them on the other side of the sheet pan.
Bake everything together: Return the pan to the oven and bake for 12–15 minutes, or until the salmon flakes easily with a fork and the vegetables are tender. If desired, broil the salmon for 1–2 minutes at the end for a caramelized golden crust.
Serve hot: Transfer salmon and vegetables to plates, drizzle with extra glaze if desired, and enjoy!