Preheat oven to 175C / 350 F on convection setting.
Take the butter out of the fridge to soften. You can also microwave for 20-30 seconds to get it soft.
Prepare your loaf pan (see recipe post for options).
If you are using whole vanilla bean, cut it lengthwise and use a butter knife to skim the seeds from the middle of the pod. Take the pod and put it in the milk, rubbing it with your fingers to get all the vanilla out of it, then discard the empty pod.
for the cake
In a small bowl combine the flour, salt, baking powder and baking soda.
In a large bowl, cream together the butter and sugar until homogenous.
Add the wet ingredients (eggs, yogurt, milk, vanilla bean extract and vanilla bean paste) and mix until incorporated.
Add the dry ingredients (flour, salt, baking powder and baking soda) and mix until just incorporated (don't overmix).
Pour the batter into the prepared loaf pan.
Bake in preheated oven for about 50 minutes.*
Check the cake at the 20 minute mark and if it's already very browned on top, then tent it with some aluminum foil, being careful not to press the foil down too hard so it doesn't stick to the top of the cake.
After 50 minutes the cake should be ready. If it still seems jiggly in the middle, use a toothpick to poke the middle of the cake and see if it comes out clean. If it isn't clean, bake another 5-10 minutes until it's set.
Take cake out and allow to cool for about 15 minutes before take it out of the loaf pan and glazing it.
for the glaze
Make the glaze right before you are going to use it (when the cake is already cool) or it can harden and get lumpy.
Mix the wet ingredients (milk, vanilla bean paste and salt) together.
Pour the wet ingredients over the powdered sugar and mix until a smooth glaze forms.
Pour the glaze over the cooled cake.
Notes
* If you are not using a convection setting, you may need to bake for longer (10-15 minutes). Check doneness with a toothpick and adjust accordingly.