Caramelize the onions: Melt 3 tablespoons butter in a 12-inch skillet over medium-high heat. Add the diced onions and cook 10–12 minutes until browned. Reserve ½ cup for the béchamel. Chill the remaining onions.
Make the béchamel: In the same skillet, melt 2 tablespoons butter over medium heat. Add garlic; cook 1–2 minutes. Stir in 3 tablespoons flour; cook 1 minute. Whisk in 2 cups milk until thickened. Remove from heat and stir in the reserved onions, 1½ teaspoons salt, pepper, and thyme.
Build the filling: Fold in the green beans and 1½ cups Gruyère. Transfer mixture to a 9"x13" baking dish.
Make the biscuits: In a bowl, whisk 1½ cups flour, baking powder, baking soda, and remaining 1 teaspoon salt. Grate in 6 tablespoons very cold butter; toss. Add the chilled onions, then ¾ cup milk. Mix gently, adding up to 2 tablespoons more milk if needed.
Top the casserole: Drop spoonfuls of biscuit dough over the filling, leaving small gaps. Sprinkle with the remaining ½ cup Gruyère.
Bake: Bake at 375°F for 30 minutes, until the biscuits are golden and the filling is bubbling.
Serving & Finishing Touches: Rest 5 minutes. Garnish with fresh thyme and serve warm.
