Cook the gnocchi in boiling salted water according to the package directions and drain.
Meanwhile, heat the oil in a large nonstick skillet over medium heat until hot. Add the onion and garlic. Cook for 30 seconds or until slightly softened. Add the mushrooms. Increase the heat to medium-high and cook for 3 minutes or until browned, stirring occasionally.
Add the chicken broth, spinach, salt, and pepper. Bring to a boil and cook for 2 to 3 minutes or until slightly reduced. Add the heavy cream and bring to a boil. Reduce the heat to medium-low and stir in the sour cream and tarragon. Cook until hot.