Half-fill a medium bowl with cold water. Squeeze in half of the lemon and stir to make lemon water.

Peel and core the apples, then cut them into pieces about 1/2 inch wide. Drop the pieces into the lemon water as you go.

Once all the apples are cut, drain them well in a sieve.

Set a medium pan over medium heat. Add 1 tablespoon of water, the maple syrup, brown sugar or monk fruit sweetener, cinnamon, nutmeg, allspice, and optional cloves. Stir until the mixture looks smooth.

Add the drained apples to the pan and toss to coat them with the spiced mixture. Cook for about 15 minutes, stirring occasionally, until most of the liquid has cooked down and the apples are as soft as you like.

If the pan gets dry, stir in another tablespoon of water or a little lemon juice. Lower the heat if the mixture cooks too quickly.

Taste the compote and squeeze in a little juice from the remaining lemon half if it needs a brighter flavor.

Stir in the vanilla, then serve the compote warm or let it cool completely.

Store any leftovers in an airtight container in the refrigerator for up to 1 week.