Combine 240 ml water and 1 cup granulated sugar in a small saucepan. Bring to a simmer over medium heat, stirring until the sugar dissolves. Remove from heat and allow to cool to room temperature.

Cook apples

Place the peeled, cored, and chopped 1 lb Granny Smith apples in a medium saucepan with the cooled simple syrup, 2 tablespoons fresh lemon juice, and 1/4 tsp salt. Cook over medium-low heat, covered, for 8–10 minutes, stirring occasionally, until apples are very tender but not falling apart.

Purée and chill

Using an immersion blender or countertop blender, purée the cooked apples and syrup until completely smooth. Taste and adjust acidity with additional lemon if needed. Stir in 60 ml Calvados. Strain the purée through a fine-mesh sieve into a bowl for the smoothest texture. Cover and chill thoroughly in the refrigerator (at least 2 hours) until very cold.

Churn or freeze

If you have an ice-cream maker, churn the chilled apple purée according to the manufacturer's instructions until it reaches a soft-sorbet consistency, then transfer to a shallow container and freeze 1–2 hours to firm. If you don't have a machine, place the purée in a shallow metal pan in the freezer and every 30 minutes scrape with a fork to break up ice crystals until you have a fine sorbet texture (about 2–3 hours).

Cider Granita (optional)

Combine 1 cup dry hard cider, 1 tablespoon sugar, and 1 teaspoon lemon juice in a shallow metal pan and stir to dissolve the sugar. Place in the freezer. After 30–45 minutes, when edges begin to freeze, use a fork to scrape and fluff the ice into crystals. Repeat scraping every 20–30 minutes until you have light, flaky crystals (2–3 cycles). Stir in 15 ml Calvados just before serving to keep texture delicate.

To Serve

Spoon one generous tablespoon of the chilled cider granita (if using) into the bottom of a chilled shot glass, then add a small scoop (about 2 tablespoons) of the apple sorbet. Gently pour or spoon an additional 10–15 ml Calvados over the sorbet so it pools slightly around it — this is the traditional 'trou' (hole) of spirit that refreshes the palate.

Garnish each glass with a small mint leaf if desired. Serve immediately as a palate cleanser between courses or as an intermezzo. For a non-alcoholic version, omit the Calvados and replace the spirit additions with 1–2 teaspoons of extra lemon juice or a splash of strong apple juice.