Cut each lobster tail in half lengthwise. Pull out the meat and save the shells. Cut the meat into 1” pieces, set in a bowl, and refrigerate.
Melt 1 Tbsp. of the butter in a small pot over medium heat. Add the lobster shells and cook until bright red in colour- about 4 minutes. Pour in the stock, bring to a simmer, and simmer 10 minutes. Strain the stock into a bowl.
Melt the remaining butter in a skillet. Add the onion, carrot, mushrooms and garlic and cook 3 to 4 minutes. Mix in the flour, tarragon and paprika and cook 1 minute more. While stirring, slowly mix in the lobster-flavoured stock. Bring to a simmer, and simmer 5 minutes. Stir in the lobster meat and simmer until cooked through, about 3 to 4 minutes. Stir in the snow peas, cream, salt and pepper, heat through 1 minute more, and then serve.
Note: To blanch the peas, plunge into boiling water 30 seconds. Cool in ice-cold water, and then drain well.