Key goals you may have in cooking brussels sprouts:
In savory applications, the most intense preparations do all three. Three common high-heat methods, from least to most involved:
Trim and halve sprouts; toss in oil and salt; roast cut-side-down on hottest oven setting until tender (but not soft).
Like #1, but improve browning by pan-roasting. That is: heat an oven-safe pan on your stovetop until it is quite hot; add oil; add sprouts, cut-side down; leave on stovetop high heat until they’ve started to brown, then toss, salt again, and move to oven until cooked through. If sprouts are small, they may be cooked through by the time their cut side browns.
Like #2, but all on stovetop (creates more contrast): once cut sides are somewhat browned, add 4-8T butter to pan (will depend on area); tilt pan and baste tops of sprouts with butter/oil until cooked through.
Deep fry trimmed+halved sprouts; drain well and salt.
In all cases, you can improve the finished sprouts by dressing them in a sauce. A squeeze of citrus and some chili is a fine start. Fish sauce is common. I like Italian agrodolce a lot with sprouts.
High heat does distort the flavor of the sprout—it completely tames the mustard note and adds a very strong caramel flavor. So, moving in the less aggressive direction:
When the sprouts are in good shape and it’s warm out, I often serve them raw: shave them with a mandoline or a sharp knife into a big bowl; dress as if they’re cabbage or another tough green.
They’re very good pickled—that mostly preserves the mustard notes.