i also find it's helpful in this recipe to take the sheet pan out about halfway through, give everything a bit of a stir, and rotate the sheet when i place it back in the oven. i dont think you lose the nice char on the broccoli and it helps prevent burning either the garlic or the broccoli.
I hear you—you could also try slicing it a little thicker than you normally would (and making sure your broccoli pieces aren't so thick they'll take a long time to roast), and also making sure there aren't any garlic slices exposed way out on their own on the baking sheet—they'll be the first to burn.
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