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Preheat the oven to 350°F. Grease a 9" or 10" tube pan or bundt-style pan; or a 9" x 13" pan.
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To make the filling: Combine the filling ingredients in a small bowl. Set aside.
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To make the cake: Beat together the butter, oil, and sugar till in a large bowl.
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Add the eggs one at a time, beating well after each addition. The batter will be thin.
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Reduce the mixer speed to low, and gradually mix in the gluten-free baking mix, sour cream, and vanilla, mixing just until combined. The batter will be stiff.
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Spoon half the batter into the pan, and sprinkle with half the filling.
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Spoon the remaining batter into the pan, and sprinkle with the rest of the filling.
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Run a knife through the batter several times to distribute the filing. Smooth the top with a wet spatula. Bang the pan on the table to settle the batter and remove any large air bubbles.
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Bake the cake 45 to 55 minutes in the tube or bundt-style pan, or until a cake tester inserted into the center comes out clean. Bake 35 to 40 minutes in a 9" x 13" pan.
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Remove the cake from the oven, loosen the edges, and allow it to cool in the pan for 20 minutes.
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Turn the cake out of the pan onto a serving plate (if you've baked it in a tube or bundt-style pan). Allow it to cool for at least 30 minutes before glazing and serving.
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To make the glaze: Combine the glaze ingredients, adding additional cream or milk, if necessary, to make a glaze with the consistency of molasses.
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Drizzle the glaze over the cooling cake just before serving; if the cake is too warm when you glaze it, the glaze will sink in.
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Serve the cake slightly warm, or at room temperature.