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.