Make the biscuits: In a large bowl combine the three flours with the sugar, the baking powder, and salt. Add the butter and blend with a pastry cutter or your fingertips until the butter is the size of peas. Chill the mixture until cold, 15 to 20 minutes.

Meanwhile, in a small bowl, whisk together the milk, eggs, and vanilla extract and chill.

Gradually stir just enough of the chilled milk mixture into the chilled flour mixture to form a dough that holds together when squeezed and is just firm enough to roll out. Knead the dough a few times in the bowl to bring it together into a ball (gluten-free biscuits require more kneading to bring the dough together). Cover and chill for at least 15 minutes or up to several hours.

Position a rack in the upper third of the oven and preheat to 375°F. Grease the bottom and sides of an 8-inch round cake pan with butter and line with parchment paper.

Make the filling: Place the raisins in a heatproof bowl and cover with boiling water. Set aside to plump, about 10 minutes, then drain well. In a small bowl, mix together the brown sugar, cinnamon, allspice, and salt.

Lightly dust a large piece of parchment paper with buckwheat flour and place the chilled dough on it. Use your hands and a rolling pin to pat and roll out the dough into a 10 by 14-inch rectangle, dusting the dough as needed to prevent sticking. If the dough cracks or breaks, pinch it back together. When the dough begins to stick to the parchment, top with a second piece of parchment and, grasping both pieces of parchment and the dough, flip it over. Gently peel away the top piece of parchment and continue rolling out the dough.

Brush the dough with the melted butter, distribute the raisins evenly over the dough, sprinkle all over with the brown sugar mixture, and press the filling into the dough with your hands.

Starting with a wider side, use the parchment to help roll the dough into a log, rolling it as tightly as possible and ending with the seam side down. Use a sharp knife to assertively cut the log crosswise into 8 equal pieces. Place one biscuit in the center of the prepared pan and the others evenly spaced around it, using a spatula if needed. Slightly flatten the tops of the biscuits. Brush the tops with milk and sprinkle with granulated sugar. Bake the biscuits until golden on top and a toothpick inserted in the center comes out with moist crumbs, 30 to 40 minutes. Remove from the oven and let cool to warm, 30 minutes.

Meanwhile, make the icing: Use the back of a spoon to mash the cream cheese and confectioners’ sugar until smooth. Whisk in the milk, a few drops of vanilla extract, and a pinch of salt, adding more milk as needed to make a thick but pourable glaze. Drizzle the glaze over the biscuits.

To serve, use a knife or offset metal spatula to coax the biscuits out of the pan.