In a large, deep skillet, bring the coconut milk and chicken broth to a simmer over medium heat. Stir in the fish sauce, garlic, ginger, chili sauce and lime juice and cook for 2 minutes.
Stir in the shrimp and cook until just opaque, about 4 minutes. Stir in the cilantro and remove from the heat. Transfer two-thirds of the shrimp mixture to a bowl; let cool.
In a large pot of boiling, salted water, cook the spaghetti until al dente; drain. Using tongs, transfer one-third of the pasta to the skillet of shrimp.
Cook one meal now: Toss the pasta with the shrimp mixture and simmer until warmed through, 1 to 2 minutes.
Freeze two meals for later: Divide the remaining shrimp mixture between 2 resealable 1-gallon freezer bags; seal. Divide the remaining spaghetti between 2 more freezer bags; let cool, then seal. Label each and freeze. THAW 1 bag each of the shrimp mixture and pasta per meal in the refrigerator overnight. Cook as directed in Step 4.