Wash and dry potatoes, then peel and chop them. Place into a large pot of cold, salted water and bring to a boil. Reduce heat and cook potatoes until fork tender, about 7-10 minutes. Remove from heat, drain and transfer to a medium bowl. Working in small batches, press cooked potatoes through a potato ricer into a large bowl. Let cool for 20 minutes.
To make herb dressing: In a small bowl, whisk together oil, balsamic vinegar, lemon juice, salt, parsley, oregano, thyme and tarragon. Set aside.
To make gnocchi: Combine the cooked potatoes, flour and egg. Transfer to a lightly floured surface and knead until dough forms. Shape dough into one long, 1/2-inch thick rope, then cut into 1/2-inch pieces to form the gnocchi. Gently roll a fork over each piece of gnocchi, leaving a soft indent.
Bring a large pot of water to a boil. Drop the gnocchi into the water and cook for 3-5 minutes, until they rise to the surface. Drain and transfer to a large bowl, then toss with herb dressing. Serve warm. Enjoy!