Melt the butter with the oil in a large skillet over medium heat. Add the shallot, garlic and red pepper flakes and cook, stirring occasionally, until the garlic is soft and aromatic, but not quite golden, about 2 minutes. Add the heavy cream and take off the heat.
Add the spaghetti to the boiling water and cook according to package directions. One minute before the pasta is done, remove 1/2 cup of the pasta water with a measuring cup and reserve. Add the sugar snap peas to the boiling water with the spaghetti for that last 45 seconds. Drain the pasta and snap peas, then add them to the skillet with the sauce. Add the lemon juice, zest, cheese and a splash of the cooking water and cook over high heat until well coated, about 1 minute. Stir in the herbs and serve immediately.