Heat the cinnamon stick, cumin seeds, peppercorns and cardamom in a small skillet over medium-low heat, stirring, until toasted, about 4 minutes. Make the brine: Combine the vinegar, 3/4 cup water, the sugar, lemon juice, 1 tablespoon salt, the ginger, chiles and toasted spices in a medium saucepan; bring to a simmer over medium heat. Cook, stirring to dissolve the sugar, 5 minutes. Pack the mango wedges into a 1-quart jar, then pour in the hot brine; let cool completely. Cover and refrigerate overnight or up to 1 week.