Combine the chopped pears and water in a small heavy-bottomed saucepan. Bring to a simmer over medium heat and cook for 10 minutes until the pears are completely soft and breaking down.

Press the softened pears through a fine-mesh sieve over a bowl. Discard the pulp. You should have about 180 ml of pear liquid.

Return the pear liquid to the saucepan. Add the sugar, cinnamon stick, and cracked cardamom pods. Stir over medium-low heat for 3 to 4 minutes until the sugar fully dissolves and the syrup thickens slightly to coat the back of a spoon.

In a separate small pan, melt the butter over medium heat. Swirl the pan every 30 seconds. The butter will foam, then the foam will subside. Watch closely at this point.

The moment the milk solids at the bottom turn golden-brown and the pan smells like toasted hazelnuts, pour the brown butter immediately into the warm pear syrup. The residual heat in the pan will keep cooking the solids if you leave them, so pour fast.

Stir in the salt and vanilla extract. Steep the spices in the syrup for 5 minutes off the heat, then remove the cinnamon stick and cardamom pods. Strain the syrup once more through the fine-mesh sieve into a clean glass jar.

Brew a double espresso shot (60 ml) directly into your serving mug. Add 2 tbsp of the pear brown butter syrup and stir for 10 seconds until combined.

Steam 200 ml of whole milk to 65 C / 149 F using a steam wand or frother. If using a frother, heat the milk separately first, then froth for 20 seconds.

Pour the steamed milk over the espresso in a slow, steady stream, holding back the foam with a spoon, then spoon the foam on top. Dust with a pinch of ground cinnamon and serve immediately.