Irish Apple Cake

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1. 1Step 1: Arrange a rack in center of oven; preheat to 350°. Butter a 9" springform pan and line sides and bottom with parchment.
2. 2Step 2: In a medium bowl, whisk granulated sugar, baking powder, cinnamon, salt, ginger, nutmeg, allspice, and 3 cups flour. Add cubed butter and incorporate with your hands until you have no large pieces left and mixture resembles wet sand.
3. 3Step 3: In another medium bowl, whisk eggs, heavy cream, and vanilla. Add to dry ingredients and mix with a rubber spatula until just combined.
4. 4Step 4: In a small bowl, toss sliced apples with remaining 3 Tbsp. flour until coated, then fold into batter. Transfer batter to prepared pan. Sprinkle with demerara sugar.
5. 5Step 5: Bake cake until apples are very tender and a tester inserted into the center comes out clean, about 1 hour and 20 minutes. Let cool completely in pan.
6. 6Step 6: In a medium heatproof bowl, whisk egg yolks and granulated sugar until lightened in color, about 6 minutes. Into a medium, heavy saucepan over medium-low heat, scrape vanilla seeds. Add pod and heavy cream. (If using vanilla extract, add once custard is removed from heat.) Cook, watching carefully, until just boiling. Remove from heat. Whisk 2 to 3 Tbsp. hot cream into egg yolk mixture until combined. Gradually add remaining hot cream, whisking constantly.
7. 7Step 7: Return custard to pot and continue to cook over medium-low heat, stirring constantly until just thickened (do not boil!). Check the consistency by dipping a wooden spoon in, then running a finger along the back; the streak should stay intact.
8. 8Step 8: Immediately remove from heat and pour through a fine-mesh strainer into a medium bowl. Let cool.
9. 9Step 9: Once cool, serve over slices of apple cake.