Combine water and salt in medium sauce pan. Bring to boil. Gradually whisk in grits. Reduce heat to low, cover pan and simmer until tender and almost all liquid is absorbed, stirring occasionally, about 8 minutes. Uncover; stir until all liquid is absorbed, about 1 minute. Remove from heat. Stir in jalapenos. Season with pepper. Let stand until just cool but not set, stirring occasionally, about 30 minutes.
Drop grits mixture by generous 1/4 cupfuls onto nonstick baking sheet forming 6 mounds. Press with fingertips to form 2-inch rounds. Let stand at room temperature until firm, about 1 hour. (Can be made 1 day ahead. Cover baking sheet with plastic; refrigerate.)
Preheat oven to 350 F. Bake cakes uncovered until hot, about 15 minutes. Meanwhile, melt butter in large skillet over high heat. Add shrimp and sausage; saute until shrimp are opaque in center, about 3 minutes. Using slotted spoon, transfer shrimp and sausage to plate. Add cream and broth to skillet; stir until lightly thickened, about 3 minutes. Add cheese; simmer until cheese melts and sauce is thick, about 2 minutes. Return shrimp and sausage to skillet. Season with salt and pepper. Remove from heat. Place 1 grit cake on each of 6 plates.
Spoon sauce over grit cakes, dividing equally. Sprinkle with chives and serve.