For the pesto: Finely cut the Parmesan and put it into a blender or food processor. Peel the garlic, tear the leaves from the bunch of basil and add both along with the oil and pine nuts. Blitz to a paste, season to taste and set aside.
For the gnocchi: finely grate the Parmesan and put it into a medium bowl. Pick the thyme leaves and add them along with the mascarpone, flour, eggs and salt and pepper. Mix together to make a soft dough. Then transfer the dough to a lightly-floured surface and knead to form a smooth ball.
Divide the mixture into 3 pieces and roll each one out into a sausage about 23 1/2 inches long. Cut each into 3/4-inch pieces to yield about 30 pieces (90 in total). Halfway through, put 2 large frying pans on over medium-high heat with a drizzle of oil and knob of the butter.
Divide the gnocchi between the 2 pans and turn down low. Leave the gnocchi to cook on one side for a minute, before carefully turning them over with a fish turner. Cook, continuing to gently turn them every so often, until they are crisp and golden all over and warmed through, 4 minutes more. If all the gnocchi didn't fit in your pans, then transfer the cooked ones into a bowl, cover with foil to keep warm and cook the remainder, adding more oil and butter as necessary.
For serving: Once all the gnocchi are cooked, stir the pesto through until evenly coated. Toss in the arugula and mix together. Then, divide among four serving plates and scatter the pine nuts over. Squeeze the lemon over the top. Give a good grind of black pepper and serve.
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