Cook butter in a medium saucepan over medium heat until butter is bubbly, golden/amber colored and caramelized. Remove from heat and stir in fresh ginger.
While butter cools, sift flour, ginger, cinnamon, baking soda, and salt into another large bowl.
Transfer butter to the bowl of a stand mixer. Mix with brown sugar and white sugar with a paddle attachment until combined. Preheat oven to 375 °F.
Add the vanilla and 2 eggs, one at a time, and mix until cohesive. It should become the consistency of cake batter.
Lastly, add the flour mixture and chopped rhubarb pieces and mix until a dough forms.
Scoop large balls of cookie dough onto a parchment lined baking sheet with an ice cream scoop. Top with a little sea salt and Demerara sugar, as well as 2-3 slices of rhubarb.
Bake for 16-20 minutes, until golden brown.