Put the potatoes in a large saucepan and add enough cold water to cover. Season with salt and bring to a simmer; cook, uncovered, until the potatoes are fork-tender, about 45 minutes.
Meanwhile, pour the heavy cream into a bowl and whip with a whisk or hand mixer until soft peaks form. Set aside.
Drain the potatoes. Hold with an oven mitt or kitchen towel and peel off the skins, then transfer the potatoes to a bowl.
Add the warm milk and butter to the bowl and mash with a potato masher or fork (or pass the potatoes through a ricer or food mill for a smoother mash). Fold in the whipped cream and pesto. Season with salt and pepper.