Preheat oven to 355F (180C).
Clean and chop rhubarb into small pieces. Set aside until ready to use.
Line a rectangular baking dish with parchment paper (8" x 13", or you can use a square 10" x 10" pan).
Melt the butter and the two types of sugar together in a small pot on the stove until it's just combined. Let it cool until it's no longer burning hot, about 15 minutes.
Add the eggs and vanilla to the butter and sugar, whisking vigorously to make sure the eggs don't scramble. Whisk together for about 2 more minutes.
Combine dry ingredients - flour and salt - in a separate mixing bowl.
Add dry ingredients into the wet, folding together with a spatula until there are no dry spots left.
Set aside a small handful of rhubarb and white chocolate to sprinkle over the top, then fold the rest of the chopped rhubarb and white chocolate into the batter until evenly distributed.
Add batter to pan, spreading evenly, then sprinkle over the reserved rhubarb and white chocolate.
Bake for 25-35 minutes (this is a wide range because ovens can vary a lot - start checking them at 25 minutes) until the edges are golden brown and the middle is just set. You can check this by poking a knife into the center - if it comes out clean with no raw batter sticking to it, it's ready.
Let cool to room temperature, then sprinkle with powdered sugar for optional decoration. Slice and enjoy!