
Make the dressing. In a small bowl, whisk the vinegar with the honey, salt, and Aleppo pepper. Whisk in the olive oil until emulsified (If using a jar, you can cover tightly with a lid and shake until olive oil is incorporated), then stir in the shallots. The dressing can be made ahead and refrigerated for up to three days.
Toast the almonds. Add the sliced almonds to a small dry skillet and set over medium heat. Toast, stirring often, for about 3 to 5 minutes until the nuts turn golden brown and fragrant. Set aside to cool.
Arrange and dress. Lay the tomato and peach wedges in an alternating pattern on a flat serving dish. Drizzle with half of the dressing. Tear the burrata into large pieces and scatter over the top. Season the burrata generously with salt. Drizzle the remaining dressing over the salad and scatter with torn mint leaves. Sprinkle on toasted almonds and serve immediately.