Remove the leaves from 4 for the thyme sprigs.
Halve and pit the peaches. Thinly slice each half.
heat 1/4 cup sugar and 2 tablespoons of butter in a skillet.
Add the thyme leaves.
Heat until just caramelized.
Lower the heat. Toss in the peach slices to coat.
Cook for 10 minutes.
Set aside and let peaches cool to room temperature.
Preheat oven to 350F. Grease & flour a bunt pan.
Whisk together the flour and baking powder. Set aside.
Cream together 1/2 cup butter, brown sugar, and chopped thyme leaves.
Add the flour mixture in thirds, alternating with the milk.
Drain any excess liquid off of the peaches and gently fold them into the batter
Transfer the batter into the prepared pan.
Bake 40 minutes or until a knife inserted in the middle comes out clean.
Transfer the cake to a wire rack fitted over a parchment lined baking sheet.
Let cool completely.
Heat the butter and sugar together in a small saucepan, stirring constantly.
When the mixture comes to a boil, remove from heat and whisk in the cream and salt.
Whisk in the powdered sugar a bit at a time until the icing stiffens but is still durable. You can adjust the consistency be adding more cream or powdered sugar as you go.
Pour the icing over the cake.
Sprinkle with extra thyme leaves before the icing sets.
Transfer to a cake plate. Cut & serve.