In a medium nonstick frying pan over medium-high heat, cook corn in butter, stirring often, until corn begins to turn brown, 2 to 3 minutes. Spoon 2/3 cup into a small saucepan. Set aside frying pan with remaining corn.
Add broth to saucepan and bring to a boil over high heat. Lower heat and simmer, covered, until corn is tender, about 10 minutes. Purée mixture in a blender, then rub through a fine strainer into a microwave-safe bowl, discarding hulls. Stir in cream. Season with 1/4 tsp. salt and 1/8 tsp. pepper; set aside.
Open up trout and season on both sides with remaining 1/4 tsp. salt and 1/8 tsp. pepper. Heat the oil in a large nonstick frying pan over medium-high heat. Protecting hands, carefully add fish skin side down (it will spatter) and cook, occasionally basting flesh with oil, until skin is well browned and crisp, 3 to 4 minutes. Reduce heat to low and continue cooking and basting until flesh is no longer pink, 3 to 5 more minutes.
Rewarm corn kernels in frying pan over medium-high heat and stir in chopped tarragon. Microwave corn sauce to rewarm. Cut trout in half with scissors.
Spoon sauce onto 2 plates and arrange a trout half on each, discarding oil in pan. Mound corn on fish and scatter with tarragon leaves. Season with more salt to taste.
Note: Nutritional analysis is per serving.