Step 1: Heat the Oven and Prepare the Pan - Preheat your oven to 425°F and lightly grease a medium baking sheet. That hotter oven is important because it helps the Brussels sprouts roast instead of turning soft and pale. I like to get the oven going before I touch anything else, because by the time the sauce is mixed and the vegetables are cut, the oven is usually ready. Give the pan a light coating of oil or cooking spray so the honey in the sauce does not cling stubbornly to the surface after dinner.
Step 2: Whisk the Honey Mustard Sauce - In a small bowl, whisk together 2 tablespoons of the olive oil, 1 tablespoon of the lemon juice, the Dijon mustard, honey, minced garlic, salt, and black pepper. Keep whisking until the honey and mustard are fully blended and the sauce looks smooth and glossy. You want the garlic distributed through the mixture rather than sitting in one clump at the bottom. At this point you will smell the mustard and garlic first, with the honey softening everything in the background.
Step 3: Coat and Arrange the Chicken - Place the chicken thighs on the prepared baking sheet, leaving a little room around each piece. Brush the honey mustard sauce over both sides of the chicken so every thigh gets a good coating. I usually finish with the chicken arranged smooth side up because that gives the sauce a nice surface to settle onto as it bakes. If any sauce remains in the bowl after brushing the raw chicken, do not save it for serving unless you cook it first. The goal here is simply to get an even coating on every piece before the vegetables join the pan.
Step 4: Season and Add the Brussels Sprouts - Put the halved Brussels sprouts in a medium bowl and add the remaining 2 tablespoons olive oil and remaining 1 tablespoon lemon juice. Toss gently until the sprouts are lightly coated, then spread them around the chicken in a single layer. When you can, turn the cut sides down against the baking sheet. That direct contact with the hot metal is what gives you those deeply browned edges that taste almost nutty and a little sweet. Avoid piling the sprouts on top of one another, since crowded vegetables tend to steam rather than roast.
Step 5: Roast Until the Chicken Is Done - Bake the pan for about 30 minutes, or until the chicken is fully cooked and the Brussels sprouts are tender with browned edges. Chicken is safely cooked when the thickest part reaches 165°F on an instant read thermometer. Depending on the size and type of thighs you use, yours may need a few extra minutes, especially if they are bone in. When the pan comes out, let the chicken rest for about five minutes before serving. That short rest helps the juices settle back into the meat while you finish getting everyone to the table.