Step 1Use a fork to blend the flour, sugar and salt in a mixing bowl. Add the shortening and butter. With your fingertips, rub the fat into the flour until the mixture is half pea-size pieces and half the texture of coarse meal.
Step 2Add the water and stir lightly with a fork until all the flour has been moistened and the mixture holds together. Divide the dough in half and make a rectangle of each piece. Wrap and chill at least 30 minutes while you prepare the fruit.
Step 1Slice the apple quarters lengthwise in half, then cut each piece crosswise into 1-inch chunks and place them in a mixing bowl. Repeat with the quince, being sure to cut out any gritty white part that lies beneath the seeds.
Step 2Blend the sugar, flour and cinnamon together. Sprinkle over the fruit and toss to mix.
Step 3Roll out the first piece of chilled dough on a floured board to 18x7 inches. Cut it in 3 (7x6-inch) pieces, then roll each out to make a 7-inch square. Repeat with the remaining chilled dough.
Step 4Heat the oven to 425 degrees. Have ready a 13x9-inch baking pan.
Step 5Working one square at a time, place some fruit in the center, scraping in a little, if any, melted sugar. Add 1/4 cup of cranberries and top with a piece of butter.
Step 6Brush the edges of the square with cold water. Bring the two opposite corners together and pinch at the top and the sides. Repeat with the other corners and sides. Set the dumpling in the pan. Continue with the remaining squares.
Step 7Bake the dumplings while you prepare the syrup.
Step 1Blend the sugar and water in a 1-quart saucepan and stir while bringing to a boil.
Step 2After the dumplings have baked 15 minutes, pour the boiling syrup over them. Return them to the oven. Spoon or brush the syrup over the dumplings after another 10 minutes. Continue to bake the dumplings until the fruit tests tender with a thin skewer, about 5 minutes more.
Step 3Cool a few minutes, then lift the dumplings onto dessert plates with a spatula. If the dumplings cool enough that the caramel hardens, return them to a 425-degree oven for 5 to 10 minutes to soften.