To a large saucepan, add the peas, water, sliced leek and thyme. Bring the pea mixture to a boil and then immediately take the pot off of the heat and let it steep for 10 minutes. Using a slotted spoon, reserve ten or so peas to use later as a garnish.
Carefully transfer the liquid to the jar of a blender, along with the roasted garlic, and blend until completely smooth, about 2-3 minutes. Salt the pea sauce to taste. I added about 1/2 teaspoon of salt. Blend the mixture once more and transfer it to a bowl.
Give the blender a wash and thorough dry. Add the goat cheese, heavy cream and pinch of salt. Blend until very smooth, about 1 minute, and set aside.
Bring a large pot of salted water to a boil. Drop the gnocchi in the water and cook them until they float to the top, about 1 minute. Transfer the gnocchi to a bed of paper towels to dry. Repeat the boiling process until you've cooked all of the gnocchi.
5. Add about 1/2-inch of olive oil to a skillet. When the oil is very hot, add the gnocchi, being sure they don't touch each other. Cook the gnocchi until they're lightly golden brown on both sides, flipping them every thirty seconds or so to ensure an even sear. Place the gnocchi on a bed of dry paper towels to drain. Repeat the process until you've seared all of the gnocchi.
To assemble the dish, add the pea sauce to a skillet and heat it until warm. Divide the pea sauce among the plates or bowls. Scoop the goat cheese sauce and place it in the center of the bowl. Arrange ten or so gnocchi onto each plate. Garnish with the reserved peas and pea shoots. Serve immediately.