Preheat the oven to 350°F (175°C). Measure and melt the ½ cup coconut oil (or have the canola oil ready). Use a pastry brush or a folded paper towel to brush the bundt pan with some of the melted oil (use part of the ½ cup listed). Dust the greased pan with a light coating of cocoa powder (from the ¾ cup in the ingredients) and tap out the excess.
In a stand mixer fitted with the paddle (or in a large mixing bowl with a hand mixer), combine 1 cup plain yogurt, 1 ½ cups sugar, ½ cup melted coconut oil, 2 large eggs, and 2 teaspoons pure vanilla extract. Beat on medium speed until the mixture is smooth and well combined, about 1–2 minutes.
In a separate bowl, whisk together 1 ¾ cups white wheat unbleached flour, ¾ cup cocoa powder, 2 teaspoons baking soda, 1 teaspoon baking powder, and 1 teaspoon kosher salt until evenly mixed.
With the mixer on low speed, add the dry ingredients to the wet ingredients and mix briefly to start combining. As the mixer runs on low, slowly pour in 1 cup freshly brewed hot coffee. Mix just until the batter is homogeneous—do not overmix.
Pour the batter into the prepared bundt pan, smoothing the top with a spatula. Bake for 50–55 minutes, or until a toothpick inserted in the center comes out with a few moist crumbs (not wet batter).
Remove the cake from the oven and place the pan on a wire rack. Let the cake cool in the pan for 10–15 minutes, then invert the pan to release the cake and cool completely on the rack.
To make the salted caramel, place ½ cup sugar in a medium saucepan over medium heat. Stir constantly with a high-heat-resistant rubber spatula or wooden spoon until the sugar melts and becomes a thick amber-colored liquid. Watch carefully to avoid burning.
Once the sugar is fully melted, add 3 tablespoons butter. The mixture will bubble vigorously; stir continuously until the butter is fully incorporated, about 1–2 minutes.
Slowly drizzle in ¼ cup half and half (or heavy cream), stirring constantly—the caramel will bubble up. Continue stirring and cook for 1 more minute to combine into a smooth sauce.
Remove the saucepan from the heat and stir in ½ teaspoon sea salt. Let the caramel sit off the heat for 2–3 minutes to cool and thicken slightly (it should still be pourable).
Drizzle the warm caramel over the completely cooled bundt cake. Let the caramel set slightly before slicing and serving.