In a medium saucepan, combine the diced peaches, granulated sugar, brown sugar, cinnamon, nutmeg, lemon juice, and vanilla extract.

Cook over medium heat for about 5 minutes, stirring occasionally, until the peaches begin to soften.

In a small bowl, whisk together the cornstarch and water until smooth. Pour the slurry into the peaches and continue cooking for another 2–3 minutes, stirring constantly, until the mixture thickens into a glossy peach filling.

Transfer to a bowl and refrigerate until completely chilled.

In a medium saucepan, combine the whole milk, granulated sugar, vanilla bean seeds, and the scraped vanilla pod.

Heat over medium heat until the mixture is steaming but not boiling.

Meanwhile, whisk the egg yolks in a separate bowl until smooth.

Slowly pour about ½ cup of the hot milk into the egg yolks while whisking constantly to temper them.

Gradually whisk in the remaining hot milk.

Pour everything back into the saucepan.

Cook over medium-low heat, stirring constantly with a rubber spatula, until the custard thickens enough to coat the back of a spoon or reaches 170–175°F.

Remove from the heat and discard the vanilla bean pod.

Fill a large bowl with ice and cold water.

Place the saucepan (or pour the custard into a heatproof bowl) into the ice bath, stirring frequently until completely chilled.

Once the custard is cold, stir in the 2 cups of cold heavy whipping cream until fully combined.

Fill a larger bowl with fresh ice and sprinkle in the kosher salt.

Nestle the bowl of ice cream base into the salted ice bath, making sure the ice surrounds the bowl.

Whisk continuously for 5–8 minutes, until the mixture becomes noticeably colder and begins to thicken slightly. It won't become whipped, but it should have a slightly richer consistency.

Pour about one-third of the ice cream base into a 9x5-inch loaf pan.

Sprinkle with a layer of crushed graham crackers.

Spoon over several dollops of the chilled peach cobbler filling.

Repeat the layers until all of the ice cream base has been used.

Finish with the remaining peach filling and graham crackers.

Using a butter knife or skewer, gently swirl the peach filling throughout the ice cream to create ribbons without fully mixing everything together.

Cover the loaf pan tightly with plastic wrap, then aluminum foil or an airtight lid.

Freeze for at least 8 hours or overnight, until completely firm.

Allow the ice cream to sit at room temperature for 5–10 minutes before scooping.

Serve with extra crushed graham crackers, warm peach cobbler filling, whipped cream, fresh peach slices, or a light dusting of cinnamon.