Add the mayo, garlic, cilantro, and basil to your food processor. Pulse until herbs have been chopped into very small piece and the mixture is blended.

Heat a nonstick or cast iron skillet over medium-high heat. Butter the inside of the sandwich rolls. Press them into the heated skillet, buttered side down, until just toasted. Set aside.

Assemble the sandwich by smearing the cilantro basil mayo on the top bun. Stack 3 slices of smoked beef, 2 slices of butter, and half the arugula on each sandwich.

Slice in half to serve.