Halve your peaches and remove the pits—look for peaches that are still slightly firm so they won't fall apart on the grill. Pat the cut sides dry with a paper towel; this helps them develop a nice caramelized surface. While you're prepping, heat your grill or grill pan to medium-high heat (around 400°F or 205°C). The grill should be hot enough that water droplets sizzle immediately on contact.
In a small bowl, whisk together the melted butter and honey until fully combined. I like to use honey that's been gently warmed so it mixes smoothly without any lumps—this creates a more even glaze. Add the vanilla bean paste and stir until it's evenly distributed throughout. Set the glaze aside within easy reach of your grill.
Brush the cut side of each peach half generously with the honey-butter glaze from Step 2. Place the peaches cut-side down on the hot grill and resist the urge to move them—let them sit undisturbed for 3-4 minutes to develop a beautiful caramelized crust. Flip each peach carefully and cook the skin side for another 2 minutes until warmed through. The peaches should be tender but still hold their shape.
Transfer the warm grilled peaches to a serving plate or individual bowls. Spoon a generous dollop of ricotta into the center cavity of each peach half—I find it's easier to do this while the peaches are still warm since the ricotta will soften slightly and meld beautifully. Drizzle the extra honey over the ricotta and around the plate, then garnish with the fresh mint chiffonade for a bright, herbaceous finish.