Preheat grill to medium-high heat (about 400°F / 200°C).
Wash peaches and pat dry.
Slice peaches in half and remove pits carefully.
Brush cut sides lightly with olive oil or melted butter to prevent sticking.
If using, mix honey with lemon juice and cinnamon; brush some onto the cut sides.
Place peaches cut-side down on the hot grill.
Grill 3–4 minutes without moving to develop char marks.
Flip peaches and grill another 2–3 minutes until tender but still holding shape.
Remove from grill and brush with remaining honey or drizzle with balsamic glaze.
Garnish with sliced almonds and fresh mint; serve warm with ice cream or yogurt if desired.