In a medium saucepan, combine the cranberries, sugar, juice or water, and zest. Set the pan over medium-high heat and bring the berries to a simmer. Cook until all the berries have burst and softened, about 10 minutes total.

Remove the pan from the heat and pass the cooked cranberries through a fine-mesh strainer into a bowl or measuring cup. Be sure to press the solids to extract as much of the smooth sauce as possible; you should be left with about 1 1/2 cups (400g to 425g) of sauce.

Stir the butter into the warm sauce until it’s melted completely.

Clean and dry the saucepan, then add the eggs and egg yolks to it. Slowly pour the cranberry sauce back into the saucepan with the eggs, whisking to incorporate.

Return the pan to medium-low heat and cook the curd, stirring constantly, until it’s thick enough that the lines made by your spoon or spatula as you stir take a second or two to disappear.

Remove the curd from the heat and pour it into a heat-safe bowl or measuring cup. If you see any small bits of cooked egg, pass the curd through a fine-mesh strainer to remove them.

In a small bowl, combine the hot water and gelatin. Add a spoonful or two of the hot curd to the gelatin, stirring to incorporate, then stir the gelatin mixture back into the curd, mixing thoroughly. Set aside while you prepare the meringue.

To make the meringue: In a large heatproof bowl or the bowl of a stand mixer, whisk together (briefly) the sugar, egg whites, and salt.

Place the bowl over a saucepan of simmering water (you should just barely see some lazy bubbles coming up) and whisk gently and continuously until the mixture reads 160°F to 165°F on a digital thermometer.

Remove the bowl from the heat and beat the meringue with a whisk or your stand mixer's whisk attachment until stiff.

Fold about a quarter of the meringue into the curd to lighten it, then fold the curd back into the meringue, mixing gently until no white streaks remain.

Pour the filling into the cooled crust and refrigerate the pie (covered with a cake cover or large overturned bowl) until set, at least 4 hours or overnight.

To make the topping: Whip the cream and confectioners’ sugar until soft peaks form.

Spread the whipped cream on top of the pie or serve it in a bowl alongside. Garnish with sugared cranberries, if desired (see "tips," below).

Storage instructions: Store the pie, covered with a cake cover or large overturned bowl, in the refrigerator for up to five days.