Preheat oven to 425 F.
While oven heats, slice broccoli into long, thin spears that include the stems. (You can also just use the top of the broccoli for florets, but the stems will cook to tender in this recipe so they look and taste delicious.) In a mixing bowl, toss broccoli spears with sliced jalapeños and a splash of cooking oil. Spread on a large baking sheet. Roast broccoli until beginning to brown in spots but not completely tender, about 10 minutes.
Meanwhile melt butter in the microwave. To the melted butter, add sweet chili sauce and zest from the lime (you'll use the lime juice later).
Remove pan from the oven and spread broccoli out to form a space in the middle. Place salmon fillets in the center of the pan. Season salmon and broccoli lightly with salt and pepper.
Pour half the melted butter mixture over the top of the salmon. Cover the entire sheet pan tightly with foil and return pan to the oven.
Roast the broccoli and salmon until the broccoli is very tender and the salmon flakes easily with a fork, about 15 minutes (for salmon that is 1.5 inches thick, adjust accordingly).
When the salmon is done cooking, pour the remaining half of the butter over the salmon. Squeeze lime juice over the salmon and broccoli.
Serve salmon and broccoli over rice with cilantro leaves on top.