Cut the dark leaves off the leeks. Slice the stalks in half lengthwise and wash between the layers well. Slice the stalks in half lengthwise again and chop into a small dice.
Place a skillet over medium heat. Add the butter and 1 tbsp olive oil along with the diced leeks. Season with a pinch of kosher salt. Sauté the leeks until they are tender, about 7 to 9 minutes. Add the minced garlic and sauté for another minute. Remove from the heat and allow to cool down.
Use a mandolin to thinly slice the potatoes, about ¼ inch thick. Transfer the slices to a bowl. Drizzle with 1 tbsp olive oil and then season generously with kosher salt and pepper. Add the chopped fresh thyme and sage. Toss the potato slices to evenly coat with the seasoning.
Preheat the oven to 400°F. Line a baking sheet with parchment paper and set aside. Unroll the puff pastry sheet onto a lightly floured counter. Dust with flour and gently roll out 2 or 3 times to widen the sheet slightly.
Transfer the puff pastry sheet to the parchment lined baking sheet. Create a half inch border around the sheet by cutting partway through the dough with a paring knife. Use a fork to dock the dough.
Spread the sour cream in a thin layer over the sheet, up to the border. Scatter the cooled leeks evenly over the sour cream. Cover the leeks with the shredded Gruyère cheese. Arrange the potato slices over the cheese, overlapping slightly.
Bake the tart for 35 to 45 minutes until the potatoes are tender when poked with a sharp knife. When the potatoes are fully cooked through, slide the tart from the baking sheet and allow to cool slightly before cutting.
Tear the pea shoots in half if desired and place in a bowl. Drizzle with 1 tsp olive oil, lemon juice and sprinkle with a little kosher salt and pepper. Gently toss and set aside.
Cut the tart into serving pieces and transfer to a serving platter. Scatter the dressed pea shoots over the tart and enjoy!