In a medium bowl, whisk together the eggs, anchovy paste, milk, salt, and several grinds of black pepper. Fold in the tuna, breaking it into pieces. Set aside.
Heat an ovenproof 10-inch nonstick skillet over medium-high heat. Add the olive oil and the butter. Once heated, add the diced potatoes. Cook for 2-3 minutes, until the potatoes are tender-crisp, then add the green beans. Cook for another 2-3 minutes, until the potatoes are tender and the green beans are tender-crisp.
Add the egg mixture to the pan, giving everything a quick stir to evenly incorporate the vegetables with the egg. Allow to cook, without stirring, for 3-4 minutes. Scatter the tomatoes and capers on top and continue to cook for an additional 3 minutes, or until the bottom and sides of the frittata have set.
Move pan to the oven and bake for 6-8 minutes, until the center is set. Use a heat-safe spatula to loosed the sides of the frittata from the pan and slide onto a serving plate.
Cut into wedges and serve hot or at room temperature. Frittata will keep for 3-4 days covered in the refrigerator.