In a saucepan, bring heavy cream to a boil. Soak gelatin sheets in cold water, squeeze well and dissolve completely in heavy cream. Whisk in grated Parmigiano. Refrigerate for at least 2 hours. Peel and dice pears and sauté in a small pan with sugar and honey.
Splash with wine and allow to evaporate until rather thick and syrupy. When the Parmigiano Reggiano mousse is firm, spoon into a pastry bag with a smooth tip. On each plate make four parallel mousse cylinders. Place two spoonfuls of pears on the mousse and drizzle with pear sauce.
Garnish with one chive strand and one Parmigiano crisp. Serve with warm bread crostini, if desired. Make Parmigiano crisps: Place one spoonful of grated Parmigiano on a sheet of parchment paper, forming a paper-thin (1/16-inch) circle.
Melt in the microwave for about 20 seconds. Mold while still warm and set aside to cool.