Either in a small bowl with a whisk or in a mini food processor, whip the mascarpone and honey together until it’s well combined and fluffy.
Heat the panini press to medium-high heat.
For each sandwich: Spread butter on two slices of bread to flavor the outside of the sandwich. Flip over both slices of bread and spread 1 tablespoon sweetened mascarpone on each.
Top one slice of bread with a layer of apples and close the sandwich with the other slice, buttered side up. Sprinkle some brown sugar on top.
Grill two panini at a time, with the lid closed, until the fillings are warmed and the bread is toasted, with a sweet crust, 3 to 5 minutes.
Top each sandwich with a scoop of vanilla bean ice cream (optional) and serve.