Preheat oven to 350 degrees F (175 degrees C). Line 2 baking sheets with parchment paper.
Combine butter, white sugar, and brown sugar in a bowl; beat with an electric mixer until fluffy. Mix in eggs, egg yolk, vanilla extract, and vanilla butter and nut flavoring. Add flour, oats, baking powder, baking soda, salt, and cinnamon; mix until dough is blended.
Fold white chocolate chips, rhubarb, and pecans into the dough. Drop dough onto the baking sheets using a 1 1/2-inch cookie scoop.
Bake in the preheated oven until bottoms are browned and edges are firm, 18 to 20 minutes. Cool on the baking sheets for 5 minutes. Transfer to a wire rack to cool.