Rinse the quinces, and clean the fuzzy layer off of their skin. Rubbing the fruit with a clean microfiber cloth while rinsing helps make the removal easier.
Cut into small pieces, removing the core and seeds.
Weigh the cut fruit. (We'll be adding an equal amount of sugar, by weight.)
Pour the fruit pieces into a powerful food processor with the juice of the lemon. (You can also add the lemon zest if you like.) Process into a puree.
If you don't have a powerful food processor, you can bake the quince pieces, at around 135ºC/275ºF until the fruit has softened, before processing them in a food processor or blender. (You can also microwave at 80% power for around 10 minutes. Stop periodically throughout the 10 minutes to mix the fruit and check its consistency.)
Pour the quince purée into a pot and add the sugar. (Use enough sugar to equal the weight of the cut quince pieces.)
Cook the mixture over low heat for several minutes, stirring occasionally, allowing the fruit to release its moisture.
Raise the temperature to medium heat. Keep simmering, uncovered, for around an hour. Keep an eye on the mixture, stirring as needed, to make sure it doesn't burn. If it begins to bubble up and spatter, you can try lowering the heat slightly or just stir it more constantly until the moisture is released. (Once this happens it will no longer spatter.)
Once the mixture is thick enough to hold a wooden spoon firmly upright, you are ready to pour it into molds. (It should also stay in place when moved to one side of the pan.) You can optionally prepare the molds with parchment paper for easier removal before pouring the mixture into them.
Let the mixture cool to room temperature. Then place in the refrigerator for 8-12 hours to set.
Slice and serve!
Choose ripe yellow fruit, when possible, for best flavor.
You can also boil the quince pieces before processing them into purée in the food processor, if you prefer. To avoid losing the pectin in the water, you shouldn't strain the fruit, but instead should cook the mixture longer until the liquid evaporates.
If you aren't happy with the consistency of the membrillo, you can bake it in the oven at around 135ºC/275ºF until it firms up. You can also add the membrillo back to a pan and cook it longer over the stove. Once thickened, you can pour it back into prepared molds.
You may reduce the amount of sugar, but I don't recommend going below 80% of the weight of the quince pieces.
At the beginning to midpoint of cooking the membrillo, it may start to form large bubbles and spatter out. To avoid this, reduce the heat slightly and continue to mix it, allowing the vapor to escape. Once it gets thicker, it will no longer do that and you can leave it alone for longer periods of time without issues (making sure it doesn't burn).
Store well covered in a cool, dry place or in the refrigerator for up to several months. For longer storage, wrap it well and freeze it.
Nutritional value is calculated on ending up with around 2.5 cups of finished paste, with a serving size of 1 Tbsp. This will vary, depending on how much liquid evaporates off.