Melt butter with the olive oil in a skillet over medium heat.
Stir in the minced garlic and cook until tender. Add the anchovies to the butter mixture. I use a potato masher and mash the anchovies. Cook a few minutes.
Add the tuna to the mixture. Stir until well combined.
Reduce heat to low.
Add the heavy cream to the skillet and heat until the mixture comes to a boil.
Serve in small hot bowls for use with the dipping ingredients. Almost any fresh raw vegetable goes well with bagna cauda.