In a large skillet, heat 2 tablespoons olive oil over medium heat and sear pork 3 to 5 minutes per side until golden.
In a large food processor or blender, add 4 tablespoons olive oil, and the next 11 ingredients (shallot through salt and pepper). Blend 1 to 2 minutes until smooth.
In a large slow cooker, add pork, ingredients from blender, beer and chicken broth. Cook on low for 8 hours until pork is cooked through.
Serve pork with slices of lime.