Trim the bases off the Brussels sprouts and cut them in half. Remove any gross outer leaves.
Heat 1 tbsp of the olive oil in a large frying pan (I like to use cast iron here) over a medium-low heat. Add the Brussels sprouts in a single layer, cut side down - you'll probably need to do cook them in two batches. Let them sit, undisturbed, until golden underneath (about 5 minutes). Flip and let cook until tender (roughly a further 5 minutes). If they still seem too crisp, cover with a lid and let cook on low for another 1-2 minutes to soften. Tip into the serving dish.
Return the pan to the heat, add the remaining olive oil and cook the rest of the sprouts, as before adding them to the serving dish too.
Return the pan to the heat and add the cooked chestnuts. Cook on high for a minute or so just to warm through, then scatter over the sprouts in the serving dish.
Return the pan to the heat. Add the torn olives and the chipotle paste and cook, stirring constantly, until coated and hot. Scatter over the sprouts in the serving dish and serve.