Preheat your oven to 325°F (163°C). Generously grease a mini bundt pan to prevent the cakes from sticking. Set the prepared pan aside while you assemble the batter.
In a large mixing bowl, combine the melted unsalted butter with 1 cup of granulated sugar and vanilla extract, stirring until well mixed. Add the eggs one at a time, beating well after each addition. Sift in the all-purpose flour, baking soda, ground ginger, ground cloves, and allspice, then mix until just combined. Gently fold in the spiced rum, Greek yogurt, and finely diced Granny Smith apple. I find folding the apple in gently helps keep the cakes tender and prevents the batter from overmixing.
Pour the batter into the greased mini bundt pan, filling each section about 2/3 of the way to ensure even rising. Bake for 27 minutes, or until a toothpick inserted into the center comes out clean. Allow the cakes to cool in the pan for 3–5 minutes, then carefully invert the pan onto a wire cooling rack. Leave the pan upside down for 5–10 minutes; the cakes should release easily. If necessary, gently shake the pan to help them out. Let the cakes cool completely.
While the cakes are cooling, measure out your caramel sauce ingredients. In a small saucepan over medium heat, melt 1/2 cup of granulated sugar, stirring constantly with a silicone spatula until the sugar clumps, then melts into a smooth, clear liquid. Remove from heat and add unsalted butter, whisking until fully combined and the mixture is amber in color. Whisk in heavy cream thoroughly, then return the pan to the heat and let the caramel bubble and smooth out for 2–3 minutes. Remove from heat again, stir in the spiced rum, and let the caramel cool and thicken for around 30 minutes. I like to use a whisk to really blend in the butter and cream—it makes the caramel extra silky.
If your cakes have cooled completely, you can reheat them briefly in the microwave for about 30 seconds to ensure they're warm and ready for topping. Drizzle a generous amount of the spiced rum caramel sauce from Step 4 over each cake. For extra indulgence, top with a scoop of vanilla ice cream and another drizzle of caramel. I find that serving these cakes warm really makes the caramel and apple flavors shine.