Preheat the oven to 375 degrees Fahrenheit and line a baking sheet with parchment paper. Cut the stems from the Brussels sprouts, then halve each sprout lengthwise. Cut the apple into small sticks and set aside. In a large bowl, toss the sprouts with olive oil, sea salt, and black pepper. Spread the Brussels sprouts in a crowded single layer on a baking sheet and roast until they have begun to darken, crisp, and caramelize around the edges — this takes around 30 minutes depending on your oven. During the last five minutes of cooking, add the apple to the top of the sheet of Brussels sprouts.
While the sprouts are cooking, combine apple cider vinegar, maple syrup, finely-minced garlic, and sea salt in a bowl and whisk to combine. Add the olive oil one tablespoon at a time while whisking continuously to emulsify. Give it a taste and correct any imbalances for sugar, vinegar, or oil. Once the Brussels sprouts are done roasting, toss them with a bit of the dressing and serve. You can add as much or as little dressing as you’d like to this dish, and keep any extra covered in the refrigerator for a week or so.