Peel and dice both peaches. Place in a food processor and pulse until the peaches are half pureed with some larger chunks left. Set the peach puree aside.
Halve the vanilla bean lengthwise and scrape the seeds into a saucepot.
Add the cream, milk, sugar, and salt and whisk to combine. Bring the mixture to a simmer, stirring occasionally to dissolve the sugar. Remove from heat.
Beat the egg yolks in a large mixing bowl. Slowly stream in the hot cream mixture, whisking constantly. Return the mixture to the pot and place over low heat.
Cook the custard, stirring constantly, until thickened (it should coat the back of a spoon).
Remove from heat and strain the custard through a fine-mesh sieve into a clean bowl. Whisk in the peach puree and cover the mixture with plastic wrap. Cool to room temperature
Chill for a couple hours in the fridge and then process according to your ice cream maker’s instructions. Once the ice cream is mostly firm, with the ice cream machine running, add in the cookie crumbs.
Freeze in an airtight container until firm. Soften for a few minutes before scooping.
I used store-bought shortbread cookies and pulsed them in my food processor until they were mostly crumbled. I left some larger chunks because I like the texture. I used roughly 8-10 cookies.