Preheat oven to 450 degrees. Line a large baking sheet with parchment paper or grease lightly with oil.
In a bowl or jar, whisk or shake together the brown sugar, hot sauce, soy sauce, rice vinegar, smoked paprika, red pepper flakes, and garlic cloves.
Pat the salmon very dry with paper towels and place in a large bowl. Pour half of the marinade over the salmon and toss to coat. Let sit 10-15 minutes at room temperature.
Place the salmon filets on the prepared baking sheet. Roast for 10-15 minutes until desired doneness is reached. If desired (and you didn't use parchment paper), switch the broiler to high for the final 2-3 minutes of roasting time to get a nice crisp.
Meanwhile, pour the rest of the marinade into a sauce pan and bring to a boil over medium-high heat. Cook, stirring frequently, until reduced to a glaze, about 5-8 minutes. The sauce will stick to the back of a spoon when it's the right consistency. Remove from the heat.
For the salsa: in a bowl, toss together the mango, cucumber, avocado, cilantro, mint, and lime juice. Season to taste with salt and pepper.
Divide the salmon and salsa amongst bowls of rice or your favorite grain.