In a large pot of boiling salted water, cook the linguine according to package directions.
Meanwhile, in a large skillet, heat the oil over medium heat. Add the garlic scapes and cook until tender, 3 to 5 minutes. Add the peas, 1/4 cup water, the mint and lavender. Season with salt and cook until the peas are bright green and crisp-tender, 1 to 2 minutes.
Drain the pasta and return it to the pot. Add the peas along with any liquid remaining in the pan and the cold butter, and swirl until the butter is creamy and coats the pasta. Season with salt and serve.