Trim the tuna: remove any tendon and bloodline and smooth the loin so it is straight.
Freeze the tuna loin for about 30 minutes to firm it, which makes it easier to slice thinly.
Sharpen your thin-bladed knife while the tuna chills.
Make the basil oil: place a few tablespoons of pesto in a mixing bowl and whisk in enough extra-virgin olive oil to reach a pourable, bright-green consistency.
Cut the caper berries in half lengthwise from the stem down and set aside.
Arrange your serving plates near your work area so you can transfer slices directly to the plates.
Remove the tuna from the freezer and, holding your knife at a slight angle, slice the loin very thinly across the grain. Lay the slices in a single layer on each plate.
Toss the arugula with a little lemon juice, a drizzle of olive oil and salt and freshly ground black pepper; set aside.
Place a few halved caper berries on each plate and drizzle the basil oil artfully over the tuna slices.
Squeeze a little lemon juice over the fish, season with a small pinch of sea salt flakes and freshly ground black pepper.
Top the center of each plate with a small handful of the dressed arugula and serve immediately.