Line a rimmed baking sheet with parchment paper or aluminum foil, and preheat the oven to 325
In a small bowl, combine the olive oil. garlic, paprika, anise, salt and pepper and mix into a paste. Rub equal amounts all over each thigh. Nestle the lemon pieces around the chicken (and whole garlic cloves if you wish)
Roast chicken thighs alone for about 20 minutes
While chicken is roasting, trim brussels sprouts in half and trim off any brown bits from broccolini stems. To make really tender broccolini I sometimes shave the stems a bit with a vegetable peeler. Toss veggies in about 2 tablespoon of olive oil with a sprinkle of salt and pepper and set aside
After about 20 minutes, remove the sheet pan from the oven and nestle in the veggies all around the chicken, taking care to try and keep veggies in a single layer. If there are pan juices, you can take some and spoon the drippings over the chicken thighs to baste them a bit.
Bake for another 20 minutes or so, until veggies are fork tender and chicken reaches 160 degrees. Squeeze juicy baked lemon juice over the thighs and veggies and spoon more drippings over everything. Serve and enjoy!