In a medium bowl, combine the brown sugar, salt, and vanilla.
In the same pot used to cook the rhubarb jam, melt the butter over medium-high heat, then pour it directly over the brown sugar mixture.
Whisk gently to combine, then vigorously for 30 seconds. The mixture will become thicker and slightly lighten in color. Add the eggs and continue whisking until just combined.
Using a flexible spatula, mix in the flour and baking powder. Before all the flour is fully incorporated, add the white chocolate and continue mixing until no streaks of flour remain.
Transfer the batter to the prepared pan and spread it evenly to the edges.
Dollop heaping teaspoons of the rhubarb jam all over the top of the batter (a teaspoon cookie scoop works well here) then use a toothpick or a butter knife to swirl the jam into the batter in a decorative pattern.
Bake the rhubarb bars for 40 to 45 minutes (if using a glass pan, 60 to 65 minutes) until the center is set, the bars are browned, and a toothpick or thin knife inserted into the center comes out with a few moist crumbs. It’s OK if the toothpick or knife isn’t clean, but you don’t want to see any raw batter.
Remove the rhubarb bars from the oven and cool them completely in the pan before slicing and serving.
Storage information: Store any leftover rhubarb bars covered at room temperature for several days; freeze for longer storage.