1. In a spice grinder, grind the peppercorns, fennel seeds and juniper berries to a coarse powder. Season the strip loin with salt and rub with the spice mixture. Let stand at room temperature for 1 hour.
2. Meanwhile, in a blender or food processor, combine the burrata with the milk and lemon juice and blend until smooth. With the machine on, add the olive oil in a thin stream. Season with salt and pepper.
3. Light a grill. Place a large pizza stone on the grate and heat until it is very hot, about 10 minutes. (To test the temperature, place a lemon slice or a few drops of water on the stone; the lemon should caramelize on contact and the water should bounce off the surface.) Set the strip loin on the hot stone and cook for about 30 minutes, turning once or twice, until the outside is richly browned and an instant-read thermometer inserted in the thickest part of the meat registers 125° for medium-rare.
4. Transfer the meat to a work surface and let rest for 10 minutes. Carve into thick slices and serve with the burrata salsa. —Chris Cosentino