Zest and juice the lemons into a small mixing bowl. Slice the green almonds 1/8-inch thick and immediately place in the mixing bowl with the lemon. Stir the almonds to coat well, as they will oxidize quickly. Liberally season with salt. Finely chop the fennel fronds. Add the fronds to the almonds. Set aside to macerate.
In a small bowl, stir together the honey, crushed peppercorns, and lemon juice.
Cut the stone fruits into halves and quarters. Dress the cut fruit with the pepper honey mixture. On the hot side of a grill or in a cast-iron pan set over high heat, place the fruit cut-side down and cook until charred. Remove fruit from the heat and allow to rest at room temperature.
Place the pieces of burrata on a serving platter. Cut into halves or quarters to suit the number of guests. Dress burrata with olive oil. Arrange the stone fruit around the burrata. Evenly scatter and arrange fennel in between the fruit and burrata. Drop small spoonfuls of the green almonds over the burrata and around the plate. Finish with crunchy sea salt, fennel pollen, and edible flowers. Serve with warm country bread.