Preheat the oven to 400 degrees Fahrenheit.
Clean the Brussels sprouts, removing any outer leaves with visible dirt or brown spots. Trim the stems, then cut the sprouts in half. Toss with olive oil and salt.
Place the Brussels sprouts on a sheet tray lined with tin foil or parchment paper and transfer to the oven to roast at 400 degrees Fahrenheit for about 20 minutes. Remove from the oven.
Meanwhile, trim the asparagus. Feel for the edge of the hard part of the stalk with your fingers, then hold on both sides and gently snap. Cut the asparagus into 1-inch to 2- inch pieces.
Toss the asparagus in olive oil and salt, then add the asparagus to the sheet tray with the Brussels sprouts. Roast for another 10 minutes.
Remove from the oven and serve.