Preheat oven to 350 degrees F.
Grease 9" round or square baking pan.
In small saucepan, add butter over medium heat.
Melt the butter, and then continue to cook and stir with a wooden spoon as the butter begins to foam, and ultimately turns from yellow to light brown and then finally an amber color. It will also release that deliciously nutty aroma. It is best to use a light colored pan so you can see the changes.
Immediately remove from heat.
In a medium bowl, combine flour, baking soda, baking powder, and salt.
In a large bowl with electric mixer, beat together the brown butter and sugar until well combined, about 2 minutes.
Add eggs, one at a time, beating until combined, and then stir in the vanilla, until just combined.
Add 1/3 of the flour mixture, then 1/3 of the buttermilk. Repeat with remaining flour and buttermilk until all is used, stirring until just combined. Don't over mix.
Fold in rhubarb.
Pour batter into prepared pan.
Make the crumb topping by combining butter, flour, brown sugar, and salt, and mixing until butter is dispersed and the consistency is crumbly. I use my fingers to do this but you can use a fork if you don't want to get messy.
Top cake with crumb topping.
Bake in preheated oven for 50-55 minutes, until tester comes out clean.
Let cool completely.
Cut into slices and enjoy!