Peel, core, and chop tart apples into small pieces. In a saucepan, combine apples, water, and lemon juice. Cover and cook over medium heat for 20 minutes, stirring occasionally.

Remove from heat and let cool slightly. Mash the apples thoroughly, then strain through a fine sieve to create a smooth apple purée.

In a separate bowl, whisk together eggs and two egg yolks until combined. Set aside.

Prepare a cornstarch slurry, if using, by whisking cornstarch with water until smooth.

In the saucepan with the apple purée, add butter and sugar. Stir over low heat until melted, then gradually incorporate the whisked eggs.

Continue to stir on low heat for 15-20 minutes until thickened. If using, add the cornstarch slurry and stir gently.

Strain the mixture through a fine sieve again and let cool at room temperature.

Transfer to a sterilized jar and refrigerate for at least 2 hours before serving.