Rinse quinces under running water, put them in a large pot and cover them with water. Bring the water to a soft boil and cook the apples for about an hour, until they are soft but not collapsing.
Remove quinces from the water and let them cool slightly, then cut them into pieces and pass them through a vegetable mill. This is a labour of love, but the result is guaranteed. The pectin will thicken the compote, allowing you to cut it into cubes.
Spoon the quince pulp into a pot and add the same weight of sugar: I had about 500 g of pulp, so I used 500 g of sugar, but it will depend on the quality of the quinces. Add also the lemon juice, which will help the work of the pectin.
Put the pot on the stove again, on low flame, bring it to a simmer and cook for about half an hour, stirring frequently with a wooden spoon, until the compote will turn into a pretty pinkish orange colour. It will be still quite soft.
Line a rectangular baking dish with parchment paper and spread the quince paste in a 2 cm thick layer. Let it cool completely, then place it in the refrigerator until completely set.