Start by preheating your grill to medium-high heat. Ensure the grates are clean to prevent the fruit from sticking. Lightly oil the grates using a paper towel dipped in vegetable oil and held with tongs.
In a small bowl, whisk together the melted butter, honey, and cinnamon if you are using it. Brush this mixture generously over the cut sides of the peach halves. This will help them caramelize and prevent them from drying out on the grill.
Place the peaches cut-side down on the hot grill grates. Grill them for about 4 to 5 minutes until clear grill marks appear and the fruit begins to soften. Flip them over and grill for another 2 to 3 minutes until tender all the way through.
While the peaches are grilling, pour the heavy cream, powdered sugar, and vanilla extract into a large chilled bowl. Beat with a hand mixer or whisk until soft peaks form. Keep it chilled until you are ready to assemble.
If desired, place the shortcake biscuits on the cooler side of the grill for 1 minute per side. This warms them through and gives them a slightly crisp texture that holds up well under the juicy peaches.
Place a warm shortcake on each plate. Top with two grilled peach halves (you can slice them if preferred). Spoon a generous dollop of whipped cream over the top and garnish with fresh mint leaves before serving immediately.