Slice Sourdough Bread into four 1/2-inch slices. Season on both sides with Olive Oil, Salt and Pepper.
Cut off the top of the Fennel bulb, right where the fronds begin. Reserve some of the wispy part of the fronds.) Then cut the Fennel bulb in half vertically, keeping the root intact on both halves.
Using a Mandoline (2.5 mm attachment), shave the Fennel bulb into thin slices.
Cut Lemon in half.
Cut Peach in half, twist and remove the pit.
In grill pan over medium-high heat, add Olive Oil and grill Sourdough Bread until you have nice grill marks on both sides (about 1-2 minutes). Remove.
Add more Olive Oil to the pan, place Peaches face down. Cook until caramelized with grill marks, about 1-2 minutes. Flip and grill for another 1-2 minutes on the other side. Remove.
Wipe out the pan if necessary. Turn down the heat to medium-low.
Add Olive Oil to the pan. Add Fennel, Salt and Pepper. Cook for about 1-2 minutes.
Add a squeeze of Lemon juice (about a teaspoon). Add a few leaves of Basil and cook until wilted. Remove.
To plate, place a bed of Fennel on the plate, along with the Bread. Slice peaches and arrange around the Fennel. (Note: you can arrange it any way you like. Even a rustic plating looks great).
Add the Burrata cheese.
Finish off with hand torn Basil leaves, Olive Oil and Fennel fronds.