scant 1/2 cup (2 oz) cornstarch
2/3 cup (2 oz) garbanzo bean flour (this will have a weirdly beany taste in the dough, but will bake off in the finished product -- you can swap out sorghum if desired)
1/3 cup (2 oz) potato starch
1/2 cup (3 oz) rice flour
1 tsp xanthan gum
1/2 tsp salt
1 Tbsp sugar
1/2 cup (aka 4 oz, aka 1 stick) non-hydrogenated (need I say it?) shortening, such as palm shortening, cut into several pieces
1/4 (aka 2 oz, aka 1/2 stick) cup non-dairy margarine (or use all shortening), cut into several pieces
~1/4 cup - 1/3 cup cold water, as needed
2/3 cup apricot jam
2/3 cup walnuts, chopped into fairly small bits
2 Tbsp sugar mixed with 1 tsp cinnamon
In a food processor or large bowl, mix together the cornstarch, bean flour, potato starch, rice flour, xanthan gum, salt and sugar (aka all the dries). Cut or pulse in the shortening and margarine until the largest bits are about the size of rolled oats -- don't overmix! If you're using a food processor, turn the mixture out into a bowl at this point. Add the cold water, bit by bit, mixing it around with your hands, until the mixture is moist enough that it comes together easily when you pinch it. Turn the dough over a time or two (aka knead very lightly), just until the elements are dispersed evenly and the dough coheres. Underkneading is better than overkneading. Divide the dough in two, and shape each bit into a chubby disk. Cover with plastic wrap or parchment (or tuck into a plastic bag, and refrigerate at least 1 hour.
When your dough has chilled, preheat your oven to 350. Line two cookie sheets with parchment or silpat liners.
Take out 1 disk of dough, leaving the other in the refrigerator. Lay out a sheet of parchment or plastic wrap, and sprinkle it lightly with the cinnamon sugar mixture (use ~1 tsp total). Place the dough on top, and sprinkle with additional cinnamon sugar. Top with another sheet of parchment or plastic, and roll out between the two until you have a circle that's ~11 inches in diameter. Spread the dough with half of the jam, sprinkle on half the walnuts, then sprinkle with a teaspoon cinnamon sugar.
Now comes the cutting and rolling! Taking a chef's knife or pizza cutter, divide the dough into 16 equal sections (just cut in half, then quarters, then eights, etc.), taking care not to slice up your countertop. Starting at the wide outer edge, roll each section towards the center to form an adorable little roll (you may need to lift the parchment/plastic to guide the cookie, so that it rolls without breaking at first). Place each cookie on the prepared sheet, making sure that the end is pinned underneath so that it doesn't unroll. When you've shaped all the cookies, sprinkle an additional teaspoon full of sugar over the tops of the cookies (that's ~1 teaspoon for the whole tray, not 1 per cookie). Place the tray in the freezer, and repeat the process with the remaining disk of dough.
After the dough has chilled for ~15-20 minutes (about how long it takes to roll, fill and shape the next batch), take the cookie sheet from the freezer and place it in the oven (and place your second sheet in the freezer for the same amount of time). Bake until the filling is bubbling and the crust has lightly colored, ~30 minutes (if the spilled jam is darkening too much at the base, move the sheet to a higher oven rack). Let sit on the cookie sheet for a minute or two, then move to a rack to cool completely. These are best devoured the day they're made, or stored in the freezer.