Put the quinces, vanilla bean pod and seeds, and lemon zest in a 4-quart saucepan and cover with water. Bring to a boil over medium-high heat. Reduce the heat to a simmer, cover, and cook until the quinces are tender when poked with a knife, about 40 minutes.
Drain the quinces in a colander and discard the vanilla bean. Purée the fruit and lemon zest in a food processor. Measure the purée by volume, return it to the saucepan, and add an equal volume of sugar. (For example, if you have 2 cups of purée, add 2 cups of sugar.)
Cook over medium-low heat, stirring with a wooden spoon until the sugar has dissolved, 1 to 2 minutes. Add the lemon juice and reduce the heat to low. Continue to cook, stirring occasionally, until the purée becomes a very thick paste, about 1-1/2 hours.
Meanwhile, position a rack in the center of the oven and heat the oven to 125°F. If your oven doesn’t go this low, use the lowest temperature possible and expect a shorter cooking time. Line an 8x8-inch glass or ceramic baking dish with parchment and grease with the butter. Pour the quince paste (don’t scrape the pot) into the dish and smooth the top with the wooden spoon. Bake until slightly dried and firm enough to slice, about 1 hour.
Remove from the oven and let cool to room temperature. Invert onto a cutting board and cut the quince paste into four 2-inch-wide strips. Wrap each strip in plastic wrap and refrigerate.
The quince paste will keep for up to 1 month.