Preheat your oven to 475°.
MAKE A SAUCE
Toss the peaches and shallots in a bowl with the olive oil and 1/8 teaspoon of the salt.
Lay the peaches and shallots on a roasting pan, cut sides down, in a single layer.
Roast the peaches and shallots long enough for the peels of the peaches to separate from the flesh, about 7 to 10 minutes, depending on the ripeness and variety of peach. The shallots are now par-cooked. Put them in a small bowl while you peel the peaches.
Peel the peaches. Then use the side of a large serving spoon and lightly crush the peaches as to create a stable bed on which to roast the lamb. But not just yet. Hold off on the roasting, please.
BROWN THE LAMB
Now, in a small bowl, combine the flour, the lemon juice, the oregano, and the sugar, and make a uniform mixture. It should look a bit like cream.
Heat a large skillet over high heat. Spray with cooking spray.
Pat the lamb racks dry.
Place the lamb racks in the skillet. Briefly brown the lamb racks evenly on all sides. You're simply browning the exterior; you're not looking to cook them through. Turn off the heat. Place the lamb racks on a plate.
Dry the lamb racks again with paper towels. Brush on all sides with the flour mixture. Place in the refrigerator for 20 minutes or so for the mixture to dry a bit.
Place the lamb racks on top of the semi-crushed peaches. Place the shallots on the roasting pan, too. Roast for about 15 minutes, or until the internal temperature of the lamb is 135°.
Remove from the oven, place the lamb racks on a cutting board, and let them rest for 10 minutes at room temperature before carving.
FINISH, CARVE, AND SERVE
With a fork, further crush the peaches and loosely combine them with the shallots.
Carve the lamb rack using a flexible boning knife, tracing right down the bone.
To serve, spoon the shallots and peaches on plates. Place the lamb chops on the plate naturally. Don't be too fussy about the placement. Spoon some of the lemony juices on top and garnish with the crumbled feta and fresh oregano leaves.