Prep Fruit: Peel, core, and cube the apples. Wash and hull the berries if using fresh, and cut any large strawberries into smaller pieces so everything cooks evenly.
2 apples, 2 cups mixed berries
Cook Fruit: Put the cubed apples, berries, sugar, and a pinch of salt in a pot with a splash of water so the fruit won't burn. (No need to defrost frozen berries.) Heat over medium, stirring now and then until it comes to a boil, then lower to low and cook until the frozen fruit has thawed and the apple cubes have softened. About 15 minutes is usually enough.
2 tablespoons white sugar, pinch salt
Adjust Flavor: Remove the pot from the heat and add about half the lemon juice, then carefully taste. If it needs more sweetness add sugar, if it needs more brightness add more lemon juice, or add a touch more salt to round the flavors—adjust until you like the balance.
1 teaspoon lemon juice
Thicken Compote: In a small bowl add the water and then the cornstarch, stirring until smooth to make a slurry. Pour about half of this slurry into the pot while stirring, return the pot to low heat, and stir until it thickens. If the compote isn’t spoonable yet, add another 1/2 to 3/4 of the remaining slurry and repeat; make more slurry if needed. Once it’s thick enough, cook about 1 more minute on low to remove any cornstarch taste.
2 tablespoons water, 2 tablespoons cornstarch
Finish and Taste: Take the pot off the heat and taste one last time. Add a little more sugar or lemon juice if needed to perfect the flavor.
Store or Serve: Use the compote right away or let it cool, then seal it tightly and refrigerate for later use.