Prep the chicken marinade. In a bowl, whisk 2 tablespoons olive oil, lemon juice, Dijon, garlic, smoked paprika, thyme, a pinch of red pepper flakes, and 1 teaspoon salt with 1/2 teaspoon black pepper.
Add the chicken and toss to coat. Marinate for 20–30 minutes at room temperature, or up to 6 hours in the fridge.
Heat the oven and grill. Set your oven to 425°F (220°C) and place a large sheet pan inside to preheat. Preheat your grill (or grill pan) to medium-high heat.
Prep the Brussels sprouts. Trim the bases, remove loose leaves, and halve the sprouts.
Toss with 1 tablespoon olive oil, 1/2–3/4 teaspoon salt, and black pepper. For extra crisp edges, spread them on the hot sheet pan cut-side down.
Roast the sprouts. Roast for 18–22 minutes, shaking the pan once, until tender with browned edges. If you like, toss with Parmesan during the last 2 minutes for a lightly cheesy finish.
Grill the chicken. Remove chicken from the marinade and let excess drip off.
Grill 5–7 minutes per side for breasts (thighs may need a couple more minutes), until the internal temperature hits 165°F (74°C). Let rest for 5 minutes before slicing.
Finish and serve. Squeeze a little fresh lemon over both the chicken and sprouts. Sprinkle with chopped parsley.
Taste and adjust seasoning with salt and pepper. Serve warm with extra lemon wedges.