Peaches and Cream, Literally
If your peaches are very sweet, you can skip the simple syrup step.
My attempt at a cooked-cream version didn't turn out as good as the classic, but feel free to try it anyway: After Step 2, simmer heavy cream with 1/4 cup sugar until slightly thickened, about 3 minutes. Remove from heat and stir in 2 teaspoons lemon juice; let cool slightly. Transfer peaches into serving glasses using a slotted spoon; pour the warm cream on top. Cover glasses with plastic wrap and refrigerate until completely chilled. Pour leftover peach syrup into a saucepan and simmer until reduced by about half, 3 to 5 minutes. Let cool briefly before spooning onto each serving.