Place the sliced almonds in a small, dry skillet over medium heat. Toast for 3–5 minutes, stirring frequently, until they are fragrant and light golden brown. Remove from heat immediately and set aside to cool.
In a small bowl, combine the minced shallot, white wine vinegar, lemon zest, sumac, smoked paprika, and sea salt. Let this mixture sit for 5 minutes to gently macerate the shallots.
Whisk the pomegranate molasses into the vinegar mixture, followed by the extra virgin olive oil, streaming it in slowly while whisking until the vinaigrette is emulsified.
Arrange the peach and tomato wedges on a large, flat serving platter, alternating them in a decorative pattern. Drizzle approximately half of the vinaigrette over the fruit.
Gently tear the burrata into large, rustic pieces and nestle them among the peaches and tomatoes. Drizzle the remaining vinaigrette over the entire platter.
Garnish by scattering the toasted almonds and gently torn large mint leaves over the top. Serve immediately.