Special equipment: a piping bag, optional
Preheat the oven to 400 degrees F. Put the phyllo cups on a baking sheet and bake for 3 minutes. Let cool.
Turn the oven to low broil.
In a small bowl, combine the brown sugar and cinnamon and mix. Slice the peaches in half, remove the pit and slice each half into 1/2-inch-thick slices. Cut the slices in thirds.
Put the cream into a piping bag or zip-top bag with the tip cut off and pipe some of the cream into each phyllo cup. Top with some peaches. Sprinkle the peaches with a pinch of the brown sugar and cinnamon mixture. Place under the broiler for 1 to 2 minutes, until the sugar melts. Remove from the oven and drizzle with amaretto.