Cut the cabbage in half through the root, then cut one half into four wedges, keeping the root intact on each wedge so the layers hold together. Season with salt and leave the wedges to sit for 5 minutes.
Heat a frying pan over medium-high heat and add a splash of oil (about a dessert spoon).
Place four cabbage wedges in the pan. If they fit snugly, they'll shrink as they cook. Monitor the oil level and add a touch more if the pan looks dry or the cabbage is charring unevenly.
Regularly flip, move, and spin the cabbage wedges to achieve an even char on all sides. The goal here is to brown the cabbage, not cook it through.
Once the cabbage wedges are evenly browned, add a small pat of butter (10-15g) and move the pan to spread it beneath the cabbage. Add a small shot of water to create steam and prevent the butter from burning.
Cover the pan with a lid (improvise if needed) and cook for 5-8 minutes over medium heat (setting 5 out of 9 on induction).
Remove the lid and cook for another 1-2 minutes until the water evaporates and you hear a frying sound. This re-crisps the cabbage edges. Remove the cabbage from the pan and set aside.
Wipe out any heavily charred bits from the pan.
Add 20-30g of butter to the pan and melt it over medium-high heat, stirring continuously until it turns a rich golden brown colour.
Add a dessert spoon of capers and the juice of half a lemon to the pan. This cools the sauce slightly and balances the flavour. Continue cooking for 1-2 minutes to enhance the caper flavour.
Remove from heat and season if using unsalted butter (salted butter needs no extra seasoning). Stir in some chopped parsley and a pinch of black pepper to finish.
Pour the lemon and caper beurre noisette over the cabbage wedges and enjoy this rich, tangy dish as a perfect side or light main course.