Preheat the oven to 350°F (175°C). Using a sharp serrated knife, slice the baguette on a sharp angle into ¼-inch-thick slices. Brush each slice lightly with olive oil. Flip the toasts over and drizzle the other side with olive oil as well. Evenly sprinkle the toasts with ¼ teaspoon of salt. Bake for 8 to 10 minutes, until the toasts are golden brown. Remove from the oven and set aside to cool.
Meanwhile, combine the cherries, brown sugar, apple cider vinegar, balsamic vinegar, 2 of the thyme sprigs, the black pepper, and the remaining ¼ teaspoon salt in a small saucepan. Cook over medium heat for 15 to 20 minutes until the cherries have softened and the cooking liquid has thickened to a syrup consistency. Remove from the heat, remove the thyme sprigs, and set aside.
To assemble the toasts, drain the burrata from the whey and cut into 12 equal pieces. Be sure to get some of the filling and outer mozzarella casing in each segment. Spread the burrata on each toast, followed by a small spoonful of the cherries. Remove the leaves from the remaining 2 thyme sprigs and garnish the toasts with the picked leaves. Top each toast with a few chopped almonds and serve immediately.