Step 1

Whisk egg yolks and 1/4 cup sugar in a large bowl. Stir cream and remaining sugar together in a saucepan over low heat; bring to a simmer, about 12 minutes. Remove from heat. Slowly pour cream mixture into egg yolk mixture, whisking constantly.

Step 2

Return mixture to the saucepan; cook over low heat, whisking constantly, until thickened and bubbly. Strain mixture through a fine-mesh sieve into a bowl, then whisk in buttermilk, vanilla, and salt. Let cool completely, at least 30 minutes. Chill at least 4 hours or up to overnight.

Step 3

Pour mixture into an ice cream maker and freeze according to manufacturer's instructions, about 20 minutes. Transfer to an airtight container and freeze until firm, about 4 hours.

Step 4

Preheat the oven to 350 degrees F (175 degrees C) for the cobbler.

Step 5

Wash the fuzz off of the peaches and cut into wedges. Toss peach wedges with 1/2 cup sugar.

Step 6

Place butter in the bottom of a 9x13-inch casserole dish and melt it in the oven, 5 to 8 minutes.

Step 7

Meanwhile, mix together flour, remaining 1/2 cup sugar, salt, and cinnamon. Stir in half-and-half, vanilla, and almond extract to form a loose batter; pour into baking dish over melted butter. Do not stir. Spoon peaches evenly over batter, without stirring.

Step 8

Bake in the preheated oven until a toothpick inserted into the center comes out clean and peaches are tender, 45 to 50 minutes. Serve warm with ice cream.