Shuck the oysters. Discard the empty shells and arrange the oysters on the half shell on a rimmed baking sheet.
Melt the butter in a medium skillet over medium heat. Add the garlic and sauté until fragrant, 2–3 minutes. Remove the pan from the heat.
In a medium bowl, stir together the bread crumbs and half of the garlic butter. Let sit until ready to use so the panko absorbs the butter.
Return the skillet with the remaining garlic butter to medium heat. Add the jalapeño, shallot, fennel, parsley, and collard greens. Cook, stirring often, for 5–7 minutes, or until the collard greens are wilted. Add the salt, pepper, and sherry. Cook for 5 minutes more to meld the flavors. Remove the pan from the heat.
Meanwhile, to the bowl with the bread crumbs, add the olive oil, Parmesan, and bacon. Toss to incorporate.
Spread a generous layer of rock salt on a large ovenproof baking dish or platter. Top the oysters with a spoonful each of the collard green mixture and bread crumb mixture. Arrange the oysters on the platter, nestling the shells into the salt. Transfer to the oven and bake for 12–15 minutes, or until the cheesy bread crumbs have browned.
While the oysters bake, make the mignonette: In a medium bowl, whisk together the peach, honey, vinegar, shallot, chives, and pepper.
To serve, top each oyster with a bit of mignonette.