For the Rum Bundt Cake:

1. Preheat the oven to 325 degrees F (160 degrees C). 
2. Melt one tbsp of butter in a small bowl, then use a pastry brush to spread the butter all over the bundt pan. Add a tbsp of flour to the pan and shake it to evenly coat the inside. 
3. In the bowl of a stand mixer, add the flour, sugar baking powder, salt, butter, and oil. Mix until fully combined. 
4. Mix in the milk and yogurt until just combined. 
5. Then, add in one egg at a time, mixing between each addition. 
6. Lastly, mix in the rum and vanilla until fully combined. 
7. Transfer the batter to the prepared bundt pan and bake for about 50-60 minutes or until a toothpick inserted comes out clean. 
8. Towards the end of the bake time, make the syrup.
9. Allow to cool in the pan for just 5 minutes (no more!) then loosen the edges with a knife and immediately turn out onto a cooling rack. 
10. While still warm, brush the syrup all over the cake.

For the Syrup:

1. Combine all ingredients in a small saucepan and bring to a boil.
2. Once boiling, turn heat down to low, stop stirring, and simmer for 6 minutes. 
3. Brush on warm bundt cake.

For the Caramel Sauce:

1. In a small saucepan, whisk together the sugar, salt, and water. Heat over medium high heat, swirling (not stirring) often to encourage even cooking. When it comes to a boil reduce heat to medium.
2. When the color turns an even medium amber color remove from heat and add the butter one tbsp at a time, whisking to combine. Whisk in the heavy cream and vanilla.
3. Allow to cool for a few minutes before pouring into a bowl to cool completely.
4. Drizzle on bundt cake when ready to serve.