1. Start by washing and slicing your peaches into wedges, removing the pits.
2. In a large skillet, melt the butter over medium heat. Watch as it bubbles and turns a lovely golden brown, releasing a nutty aroma.
3. Add the brown sugar, stirring gently until it dissolves into the butter.
4. Carefully place the peach slices into the skillet, ensuring they are evenly spread out. Cook for about 3-4 minutes on each side, until they are tender and caramelized.
5. Sprinkle in the ground cinnamon, vanilla extract, and a pinch of salt. Stir gently to coat the peaches evenly.
6. Let everything simmer for another minute, allowing the flavors to meld together beautifully.

As you cook, remember to keep an eye on the heat. You want a gentle sizzle, not a furious boil. This will ensure the peaches cook through without burning. I learned this the hard way during my initial cooking experiments, proving once again that gentle patience often yields the best results.