Preheat the oven to 450° F. Line a baking sheet with parchment paper or grease with oil.Add the chicken and egg to a bowl. Toss to combine. Add the cornflakes, flour, and a pinch of salt to another bowl. Dredge the chicken in batches through the crumbs, tossing to coat. Place the chicken on one side of the prepared baking sheet. Drizzle with olive oil. Add the Brussels sprouts and shallots to the other side of the pan and toss with 2 tablespoons oil, salt, and pepper. Bake for 20 minutes, until the chicken is cooked through. Reduce the oven temp to 400° F.Meanwhile, make the sauce. Combine all ingredients in a bowl until smooth and creamy. If the sauce stiffens, warm in the microwave or on the stove. Spoon the sauce over the chicken, coating each piece. Toss the sprouts with 1 tablespoon oil. Return everything to the oven for 3-5 minutes. Serve the chicken with extra sauce and the Brussels sprouts on the side. Top with fresh thyme.