Rinse the quinces and rub off any fuzz. Quarter them, cut out the cores and seeds, and cut away any bruised or dark spots. Leave the skins on.

Put the quinces in a large Dutch oven with the water. Cut a round of parchment paper to fit inside the pot and lay it on the surface of the water.

Bring it to a boil over high heat, then cover the pot, turn the heat to medium-low, and simmer about 1 1/2 hours, until a knife slides into the quinces easily.

Drain the quinces in a colander set over a large bowl, saving the cooking liquid. You should have about 5 cups.

Pour the liquid back into the pot and boil it, uncovered, over medium-high heat until it's down to about 3 cups, 12 to 15 minutes.

Meanwhile, purée the cooked quinces in a food processor until completely smooth, about 45 seconds, scraping down the bowl as needed.

Press the purée through a fine-mesh strainer a little at a time, and discard the bits of skin and fiber. You should have about 4 cups of purée.

Heat the oven to 350°F with a rack in the middle. Grease an 8-inch square baking pan and line it with parchment paper.

Stir the purée into the reduced liquid in the pot, then add the sugar and lemon juice. Bring it to a boil.

Turn the heat to medium-low and simmer, stirring now and then, until the mixture darkens, thickens, and starts to spatter, about 30 minutes.

Move the uncovered pot to the oven and bake for 1 to 1 1/2 hours, stirring and scraping down the sides every 15 minutes. It's done when it has turned deep red to rusty brown and a spatula leaves a clear trail across the bottom of the pot.

Scrape the paste into the lined pan and smooth the top. Let it cool completely on the counter, then refrigerate it until firm, at least 4 hours.

Turn the pan over onto a cutting board and peel off the parchment. Cut the paste into bars or squares with a heavy knife, rinsing the blade in cold water between cuts.

Wrap each piece in parchment paper. For anything you'll keep longer than a month, add a layer of plastic wrap over the parchment.