Zest the lime directly into a medium bowl, then cut the lime in half and squeeze the juice into the same bowl. Mince the shallot, garlic, and ginger, keeping them separate for now. Finely chop the peanuts and set aside. This prep work ensures everything is ready when you need it and prevents scrambling during cooking.
Heat 3 tbsp olive oil in a small pot over medium heat. Add the minced shallot, garlic, and ginger, cooking for 2-3 minutes until fragrant and lightly softened. Stir in the chopped peanuts and 2 tbsp honey, cooking for 1 minute more. Pour this warm mixture into the bowl with the lime zest and juice, then stir in the sambal oelek and toasted sesame oil. Season with salt and pepper to taste. This sauce can be made ahead and served at room temperature—I like to let it sit for a few minutes so the flavors meld together beautifully.
In a small bowl, whisk together the white miso paste, 1 tbsp honey, and 1 tsp soy sauce until smooth. Pat the salmon fillets dry with paper towels, then brush the miso glaze evenly over the flesh side of each fillet. Toss the broccoli florets with 2 1/2 tbsp olive oil, salt, and pepper in a separate bowl. I find that getting the miso glaze on the salmon early allows it to slightly set and adhere better during grilling, giving you better flavor transfer.
Preheat your grill to high heat and oil the grates well to prevent sticking. Once hot, place the broccoli florets directly on the grates. Cook for 6-8 minutes total, turning occasionally with tongs so they develop charred edges on all sides while remaining tender inside. Transfer the grilled broccoli to a serving platter and tent loosely with foil to keep warm.
Place the miso-glazed salmon fillets skin-side up on the hot grill. Cook for 2-3 minutes without moving them—this allows a nice sear to develop on the flesh side. Carefully flip each fillet so the skin side now faces down and cook for another 7-10 minutes until the internal temperature reaches 145°F (63°C) at the thickest point. The salmon will continue cooking slightly after you remove it from heat, so don't overcook it. Transfer to the platter with the broccoli.
Arrange the grilled salmon and charred broccoli on serving plates. Drizzle or spoon the peanut sauce from Step 2 over the salmon and alongside the broccoli. Serve immediately while everything is still warm.