Melt 1 TBS butter over medium low heat in a skillet.
Dredge fish in the flour mixture and place into the buttered skillet. Cook until golden brown on the first side. Flip fish and add another TBS butter to the skillet. Cook again until golden brown, about 5 minutes per side. Remove fish from pan.
Add garlic and remaining 1 TBS butter to the skillet. Saute until fragrant and just starting to brown. Mix in dry white wine and let it reduce in half. Mix together broth and ½ tsp flour. Pour into skillet and bring to a simmer. Let it reduce in half, stirring almost constantly. Turn off heat and mix in capers and fresh lemon juice.
Meanwhile, steam green beans by microwaving until just bright green, about 1 minute.
Serve sauce drizzled over the fish with rice and green beans.
Recipe by Alison's Allspice at https://www.alisonsallspice.com/trout-piccata-with-green-beans-and-rice/