Soak twelve 6” long bamboo skewers in water for 20 minutes.

Meanwhile, put the potatoes in a medium saucepan and add salted water to cover. Bring to a boil over high heat. Reduce the heat to a simmer and cook until just tender, 10-5 minutes. Be careful not to overcook. Drain.

Combine the potatoes, beef, tomatoes, and olive oil in a large bowl. Toss to coat evenly. Thread 1 chunk of meat, 1 potato, and 1 tomato onto each skewer, piercing the tomatoes lengthwise. Set aside.

For the aioli: In a blender or food processor, puree the egg yolks, mustard, lemon juice, and garlic until smooth. With the machine running, gradually add just enough canola oil in a slow, steady stream until the mixture is thick and emulsified. Stir in the tarragon. Season with salt and pepper to taste.

Preheat a gas grill to medium-high. Season the skewers with salt and pepper. Place on the grill, cover, and cook until seared, 1-2 minutes on each side. Arrange 2 skewers on each of 6 small plates. Serve with the aioli in small bowls on each plate.