To create the brown butter: In a medium saucepan- melt 1/2 cup butter on medium-high heat. After 2-3 of boiling, foam will begin to form. After another 2-3 minutes, the foam will separate and brown speckles will appear at the bottom of the pan. Swirl the pan a few times to ensure the brown speckles have formed and take the butter off the heat and pour in a medium glass bowl and place in the refrigerator to cool and solidify for 1-2 hours. To speed up the process- place in the freezer for 30 minutes then sit out to come to room temperature. You want the butter to be solidified yet spreadable and softened.
Preheat the oven to 350°F degrees. Prepare a 10 inch bundt pan by brushing the inside (into all of the nooks and crannies) with 1 tablespoon of melted butter and a pastry brush, then lightly dust the buttered pan with an even layer of flour- dust off excess flour into trash can (not sink).
In a medium bowl- combine all-purpose flour, chai spice, baking powder, salt and whisk to combine. Set aside
In a stand mixer fitted with a paddle attachment- beat butter(s) and sugars on medium speed for 2-3 minutes or until light and creamy. Scrape down the sides of the bowl.
In a medium bowl- combine sour cream, eggs, vanilla, and sweetened condensed milk. Whisk until combined. Add wet mixture to the butter(s) & sugar mixture and mix on medium speed for 1-2 minutes until combined. May look lumpy or curdled but it will come together once you add the flour.
Add dry ingredients to wet ingredients and mix on low speed for 30 seconds- careful to not over mix the batter. Stop the mixer when a few ribbons of flour are visible and finish by folding the batter with a spatula.
Evenly distribute the cake batter into the prepared cake pan and bake for 50-55 min. Or until a toothpick inserted comes out clean.
Place on a cooling rack for 10 minutes in the pan before turning the cake pan upside down to release the cake. Allow to cool for 30 minutes before serving.
To prepare the glaze: In a medium saucepan on medium combine the sweetened condensed milk, butter, sugar and salt and bring to a boil. Stirring constantly for 3-5 minutes. Take the saucepan off the heat and add vanilla and confectioners sugar- whisk until smooth. Immediately pour glaze over the bundt cake and serve.