For the Cake: Adjust oven rack to center position and preheat oven to 325°F. Grease a 10-inch bundt pan.
Combine flour, sugar, baking powder, and baking soda in a medium bowl.
Whisk until homogenous.
Add half-and-half, butter, and eggs. Beat using a handheld electric mixer until combined, and pour batter into pan.
Transfer to oven and bake until a toothpick inserting in the center comes out clean, about one hour.
Combine butter, sugar, and vanilla in a small saucepan over medium heat. Stir continuously until completely melted and combined. (Do not allow glaze to boil.)
Assembling the Cake: While the cake is still warm and in the pan, use a wooden skewer to poke 8-10 small holes in the cake bottom.
Pour warm glaze slowly over cake. Allow to cool completely and serve.