In a large bowl, toss trimmed and halved Brussels sprouts with 2 tbsp olive oil. Arrange them in single layer , cut sides down, in a 12-inch skillet. Drizzle with 3 tbsp olive oil on top of the sprouts and use a tong to gently move/wiggle the sprouts so that the oil seeps underneath. Combine lemon juice with salt and pepper. Set the mixture aside.
Cover and start the skillet cold (i.e. not preheated) with the sprouts over medium-high heat. Cook until the sprouts are in bright green color and cut sides have started to show light brown, about 5 minutes.
Uncover and continue to cook until cut sides of sprouts are evenly browned and in deep golden brown color and with little to no resistance when slides in a paring knife, about 2-3 minutes. Pay attention to the stovetop temperature and check the sprouts often so they don’t get overcooked or burnt.
Transfer sprouts to a large serving plate or bowl, the sprouts aren’t seasoned at this point. Before serving, add lemon juice mixture, toss and taste for more salt, pepper, or lemon juice. Sprinkle with Paleo Parmesan Cheese before serving.