In a medium skillet or cast iron skillet, heat olive oil and melt butter over medium heat. Add onions. Toss onions to coat.
Let onions cook, without stirring, for about 5 minutes. After 5 minutes, give the onions a stir and add a pinch of salt. Let onions cook for another 5-7 minutes, without stirring.
At this point, remove skillet from heat momentarily, and add balsamic vinegar. Stir to incorporate. Place skillet back onto heat and continue cooking until onions are caramelized and broken down, about another 10 minutes or so. Remove from heat and set aside until ready to build pizza.
Place unbaked pizza crust on a cookie sheet or pizza stone and bake for 10 minutes. Remove from oven.
Evenly spread apple butter over crust and sprinkle a pinch of red pepper flakes over the apple butter. Spread caramelized onions over apple butter, and then sprinkle chopped bacon and pecans evenly over the onions. Top with shredded Gouda. Place in oven (still at 450 degrees F) and bake for an additional 8-12 minutes, or until cheese is bubbling and browning.
Remove from oven and let sit for about 5 minutes before slicing.
Slice pizza and top each slice with fresh baby arugula to finish.