In a medium saucepan, combine 2 cups of heavy cream and 1 cup of granulated sugar over low heat. Stir gently with a whisk until the sugar fully dissolves, about 4-5 minutes.

Remove the saucepan from the heat and immediately whisk in the fresh juice of 4 lemons, ensuring it's well incorporated.

Carefully pour the creamy lemon mixture into your chosen cups or ramekins, filling them about three-quarters full and chill for at least 4 hours, preferably overnight.

In a mixing bowl, cream together 1 cup of softened butter and 1/2 cup of sugar until light and fluffy, roughly 3-5 minutes.

Gradually mix in 2 cups of all-purpose flour until just combined, forming a soft dough.

Divide the dough into two logs, wrap tightly in plastic wrap, and chill in the refrigerator for at least 30 minutes.

Preheat your oven to 350°F (175°C). Unwrap and slice the chilled dough into 1/4-inch thick pieces and bake for 12-15 minutes until lightly golden.

Serve the chilled possets accompanied by the crispy shortbread dippers.