Combine flour, salt, and baking powder in a food processor or mixer.

Add water and olive oil.

Process until dough is smooth and elastic.

Knead briefly on a floured surface and shape into a ball.

Cover and let rest for 20 minutes.

Cut dough into 8 pieces and cover all but one.

Shape the exposed piece into a ball and roll it into an 8-inch circle.

Place the circle of dough on a plate covered in wax paper.

Repeat with remaining dough, separating each circle with wax paper.

Preheat a skillet over medium-high heat.

Test heat by flicking water droplets onto the skillet until it sizzles.

Cook a circle of dough in the hot skillet for about 30 seconds per side, until golden brown.

Place cooked piadina on foil in the oven to keep warm.

Spread goat cheese on half of each piadina, and place arugula on top.

Fold the piadina in half and serve.