Grits: Bring 3 cups water to a simmer in large saucepan. Gradually whisk in grits. Turn heat to low; gently simmer until grits begin to thicken. Continue cooking, stirring often and adding water by 1/4 cups if too thick, until tender, about 1 hour. Stir in cheese, butter, and jalapeno, then cream. Season with salt and pepper. Keep warm.
Shrimp: Meanwhile, heat a large heavy skillet over med heat. Add tasso; saute until fat begins to render, about 5 minutes. If tasso is lean add oil to skillet. Add garlic and 1 tbsp. butter, stir until butter melts. Add shrimp. When garlic begins to brown, add beer and stock. Simmer until shrimp is cooked through, about 2 mintues. Remove from heat; set aside.
Heat large nonstick skillet over medium heat. Add remaining butter to skillet swirl to coat bottom of pan. Crack eggs into pan and cook until whites are just set but yolks still runny.
Divide grits amount bowls, forming a well in center. Spoon shirmp mix into center of grits and top with egg. Sprinkle tarragon over.
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