Heat the oven to 220C / 425F. Line a sheet pan (33 x 46 cm / 13 x 18-inch) with parchment paper.
Trim the stem ends off the brussels sprouts and halve them lengthwise. Discard any loose, yellowed outer leaves.
Toss the halved sprouts with olive oil, salt, and pepper in a large mixing bowl. Spread them cut-side down on the sheet pan in a single layer, leaving space between pieces so they roast instead of steam.
Roast for 20 to 25 minutes, flipping once at the halfway mark, until the cut sides are deeply browned and the outer leaves are crisp-edged.
While the sprouts roast, melt the butter in a 1-quart / 1L saucepan over medium heat. Add the garlic and cook for 30 seconds until fragrant, not browned.
Stir in the maple syrup, balsamic vinegar, and red pepper flakes. Simmer for 2 to 3 minutes, until the glaze thickens slightly and coats the back of a spoon.
Pull the sprouts from the oven and pour the warm glaze over them directly on the pan. Toss with tongs to coat every piece.
Return the pan to the oven for 3 to 4 minutes to let the glaze caramelize on the edges. Watch closely here, the sugars can burn fast once they hit the hot pan.
Transfer to a serving platter, scatter the toasted pecans over top, and finish with a pinch of flaky salt. Serve right away while the edges are still crisp.