Apple Pecan Pound Cake with Caramel Glaze

Makes 1 cake to serve 8

Apple-Pecan Cake:
1 cup pecan pieces
8 ounces (2 sticks) unsalted butter, at room temperature, plus more for coating the pan
1 1/2 cups sugar
2 cups all-purpose flour, plus more for coating the pan
2 teaspoons baking powder
1 teaspoon coarse kosher salt
1 teaspoon cinnamon
1/2 cup whole milk Greek yogurt
1/4 cup whole milk
1 teaspoon vanilla extract
4 large eggs, at room temperature
3 Granny Smith apples, peeled

Caramel Glaze:
1 cup sugar
1/4 cup water
1/2 cup heavy cream
2 tablespoons unsalted butter
1 tablespoon spiced dark rum (optional)
1/4 teaspoon sea salt

Heat the oven to 350° F. Lightly coat a bundt pan with softened butter and dust with flour, shaking off the excess.
Spread pecan pieces on a baking sheet and toast in oven until golden and fragrant, about 5-8 minutes. Remove and let cool, then roughly chop.
Combine butter and sugar in the bowl of a stand mixer fitted with the paddle attachment (or use a hand mixer). Beat on low speed to combine, then increase to medium speed and beat until light fluffy, about 3 minutes. Scrape down the bowl as needed. Add the eggs one at a time, beating well after each addition.
Grate the apples on a box grater (discard the core). You should have about 2 cups of grated apple. Add to the stand mixer and stir on low speed just to combine.
In a separate bowl, whisk together the flour, baking powder, salt, and cinnamon.
In a liquid measuring cup or bowl, whisk together the yogurt, milk, and vanilla extract.
With the mixer on low speed, add half the dry ingredients, then the yogurt-milk mixture, then the remaining dry ingredients. Mix just until incorporated, scraping down the bowl as needed. Add pecans and stir on low speed, just to combine.
Pour batter into the prepared bundt pan and bake until golden brown and a cake tester inserted into the center comes out clean, about 60-70 minutes. Let cool in the pan for 10 minutes, then flip onto a wire cooling rack set over a baking sheet.
Meanwhile, make the caramel glaze. In a small heavy-bottomed pot, stir together sugar and water. Cook over medium-high heat without stirring until the sugar turns a deep amber color, about 10 minutes. Remove from the heat and quickly whisk in the cream and rum (if using). Be careful as it will bubble up. Whisk in butter and sea salt. Transfer caramel to a glass or metal bowl to cool. When it is slightly warmer than room temperature, thick but still pourable, pour generously over the top of the cake, letting it soak the cake and drip down the sides.
Store in an airtight container at room temperature for up 2-3 days.