Preheat broiler with rack set in top third of oven.
Toss peppers and asparagus in 1 tbsp. oil and spread out on a rimmed baking sheet. Broil, turning often, until starting to soften and brown slightly, 6 minutes.
Whirl garlic, rosemary, salt, pepper, chile flakes, and goat cheese in a food processor until just combined.
Spoon about 1 tbsp. cheese mixture into each pepper half and top with asparagus. Drizzle with remaining 1 tbsp. oil.