Boil beans in a pot of salted water, 2 minutes. Drain; run under cold water.
In a skillet, heat 1 tbsp. EVOO over medium-high. Add chicken; season and cook, turning once, 8 minutes. transfer to a plate.
Add 1 tbsp. EVOO and mushrooms to skillet; cook over medium-high, 4 minutes. Add shallots, garlic and thyme; stir 2 minutes. Add wine; simmer until evaporated. Sprinkle with flour and stir to combine. Stir in half-and-half; bring to boil. Reduce heat. Simmer, stirring, until sauce thickens, 2 minutes. Let cool 15 minutes.
Preheat the oven to 450 degrees . Stir beans and chicken into sauce. Season; transfer to a foil-lined 2-qt. baking dish.
Toss cheese with panko and 1 tbsp. EVOO; sprinkle over casserole. Bake until golden, 15 to 20 minutes. Let stand 10 minutes before serving.
