Special equipment: Four 8-ounce mason jars.
Making the chestnut cream: Simmer the chestnuts in the cream in a small saucepan over low heat for 30 minutes. Transfer the chestnuts and cream to a food processor and puree until smooth. Strain through a fine mesh sieve, using a rubber spatula to force the chestnut cream through. Whisk in the pear syrup and vanilla extract. Chill the mixture.
Making the whipped mascarpone cream: Blend the mascarpone, honey and cinnamon in a medium bowl. Whip the cream and gently fold into the mascarpone mixture.
To an 8-ounce mason jar, add 2 heaping tablespoons of the whipped mascarpone cream and the same quantity of diced pear and chestnut cream. Repeat with the pears, and finish with the whipped mascarpone cream. Drizzle with a teaspoon of the honey and sprinkle with one quarter of the crushed shortbread cookies. Repeat with the remaining mason jars. Serve.
This dessert can be made several hours ahead. Assemble, minus garnishes, and chill. Just before serving, garnish with honey and cookies.