Brush peach halves with oil and place on a medium-hot grill. Grill for several minutes, then flip and grill the other side for several minutes more. When done, the peaches should be soft, with charred marks. Set aside to cool.

Pull the skins off the peaches and discard. Chop into pieces and place in a bowl. Cover and refrigerate, reserving the equivalent of 1 peach for the custard.

Combine heavy cream, half-and-half, vanilla bean, and reserved peach in a heavy-bottomed saucepan.

Place over medium heat and bring to a simmer (about 170°F). Cover and steep for 30 minutes.

Remove vanilla bean pieces and transfer the mixture to a blender. Blend smooth, strain, and return mixture to a clean saucepan.

Add 1/4 cup of sugar and heat on medium until sugar is dissolved and liquid is hot (about 160°F).

Whisk together egg yolks and remaining 1/4 cup sugar. While whisking, slowly add hot liquid. Continue until all liquid is added, then transfer back to saucepan.

Heat custard on medium until thickened enough to coat the back of a spoon (165°F).

Strain into a clean bowl and refrigerate overnight.

Set up an ice cream machine and churn custard according to the manufacturer's directions. Once churned, fold in peaches, transfer to an airtight container, and freeze.