Preheat the oven to 325 degrees F.
Place the quince in a cast iron casserole and roast in the oven until they are soft and collapsing and their skins are just bursting, about 30 to 40 minutes.
Once the quince are cool enough to handle, remove the skin and cores and press the flesh through a sieve, transferring it to a saucepan with the brown sugar and lemon juice and, over high heat, bring the ingredients to a boil, stirring with a wooden spoon. Lower the flame and cook the quince, still stirring, for 5 minutes, then remove from heat and allow to cool.
In a medium bowl, combine the rum and cream and beat to form stiff peaks. Lighten the cooled quince with a third of the beaten cream, then gently fold the quince into the remaining cream.
Divide the mousse out into 8 (4-ounce) ramekins, cover tightly with plastic wrap, and refrigerate for several hours. Serve chilled.