Preheat oven to 400ºF (200ºC). Toss the potatoes in the olive oil and spread in an even single layer on an aluminum foil-lined baking sheet. Season with salt and pepper and roast until golden brown and crisp, about 35 minutes.
Add the roasted potatoes to a medium mixing bowl and toss with the pesto.
To serve, scoop potatoes into tortillas and top with tomatoes, goat cheese, radish and basil. Serve immediately.