Mince the garlic cloves and set aside. Juice half the lemon and zest it into a small bowl, then slice the remaining lemon half into thin rounds for garnish. Trim the green beans and snap them into 2-inch pieces. Pat the salmon fillets dry with paper towels—this helps them cook more evenly in the foil packets. Having everything prepped and ready before you start assembling ensures a smooth cooking process.
In a small bowl, whisk together the melted butter, lemon juice and zest from Step 1, minced garlic, smoked paprika, salt, and pepper. Stir in the fresh dill. Set aside until ready to use. I like to make this sauce first so the flavors have time to meld together while I'm preparing the foil packets.
In a medium bowl, toss the trimmed green beans from Step 1 with the olive oil, 1/2 teaspoon salt, and 1/2 teaspoon cracked black pepper until evenly coated. This light seasoning allows the butter sauce to be the star of the dish without the beans competing for flavor.
Cut four 14-inch pieces of foil and place them shiny-side down on a work surface. Divide the seasoned green beans from Step 3 evenly among the foil pieces, spreading them in the center of each piece. Place one salmon fillet on top of the beans on each foil packet. Drizzle the herb butter sauce from Step 2 evenly over the salmon and beans, then add a few lemon slices from Step 1 to each packet. Optional: add 1/2 tablespoon of dry white wine to each packet for extra moisture and flavor.
Fold the foil over the salmon and vegetables to cover completely, then crimp and seal the edges tightly by folding them repeatedly, working your way around each packet. Make sure there are no gaps—this traps the steam and cooks the salmon gently and evenly. I like to create packets that are well-sealed but not crushed, so steam can circulate properly inside.
For grilling: Preheat your grill to medium-low heat. Place the sealed foil packets directly on the grill grates and cook for 13-16 minutes total, carefully turning each packet over halfway through (around the 7-minute mark) using tongs. For baking: Preheat your oven to 400°F, place the packets on a baking sheet, and bake for 20-25 minutes until the foil is puffed and the salmon is cooked through. The salmon is done when it flakes easily with a fork and has reached 145°F internally.
Carefully open each foil packet from the top, being cautious of the hot steam that will escape. Transfer the contents to serving plates or keep in the foil packets if desired. Garnish with additional fresh dill if you'd like, and serve with lemon wedges on the side for extra brightness.