Combine the milk and cream in a medium saucepan and bring to a simmer, stirring often, over medium heat. Add the peach leaves and submerge as much as possible under the liquid. Allow to steep for 5 minutes and then promptly remove with a slotted spoon.
In a large bowl, whisk together the sugar, eggs and salt until fully combined. Ladle about 1/2 cup of the steeping liquid into the egg-sugar mixture and whisk to combine. Repeat with another 1/2 cup, whisking to combine. Then pour in the remaining liquid and whisk to combine again.
To make the custard, set up a double boiler (see recipe notes for additional details). Place the bowl with the milk-cream-sugar-eggs mixture over a saucepan with 1-2" of simmering water and stir constantly, ensuring that you get into any corners or edges of the bowl. This is where an instant read thermometer is a must - you will want to test the temperature every couple of minutes until it reaches 175°F (it should take about 10-15 minutes). If you don't have a thermometer, you can always test your luck and do it by sight. You will want to cook it until it reaches a nappe consistency - dip a spoon in the custard, turn it over and draw your finger across the back. If you have a clean line, it's ready. Remove from heat and add the vanilla extract, stirring to combine. Place a piece of plastic wrap directly on the surface to prevent a skin from forming. Allow to cool on the counter and then transfer to the refrigerator until completely chilled - 8 hours to overnight.
To make ice cream, follow the manufactures instructions for your ice cream maker.
Using a double boiler is the best way to slowly cook a custard without the danger of curdling. To set it up, find a medium to large saucepan that will hold a mixing bowl on top while maintaining 2-3" between the bottom of the bowl and saucepan. Ideally, the majority of the sides of the bowl will set inside the saucepan (if only the bottom of the bowl sits inside the saucepan, it will take for.ev.er to cook).