Preheat oven to 400 degrees. Make the toast by first brushing the baguettes with oil then transferring to a baking sheet and baking until just browned (2-5 minutes on each side).

Wrap the bay leaf, rosemary, and peppercorn in a cheesecloth and tie tightly to create a cheesecloth pouch. Place the wrapped herbs in a medium saucepan with the cherries, sugar, alcohol, salt, and 1/2 cup water. Bring to a boil over medium-high heat, reduce to a simmer, and let cook until the cherries burst and soften, about 10 minutes. Transfer the cherries to a bowl and continue to let the liquid mixture simmer until it reduces to a syrup, about 15 more minutes. Remove from heat and let cool slightly. Add the cherries back to the syrup mixture.

Top the mozzarella or burrata with the cherry compote and finish with lime zest. Serve over the freshly toasted bread.