Heat oven to 375°F. Lightly grease a 9x13-inch baking dish.
Melt butter with 1 tbsp olive oil in a large skillet over medium-low heat.
Cook onions with 1 tsp salt until deep golden, 20–25 minutes, stirring occasionally.
Stir in thyme and garlic. Cook 1 minute until fragrant.
Deglaze with sherry. Simmer until almost dry, scraping up browned bits.
Sprinkle flour over onions. Cook 1 minute, stirring constantly.
Whisk in broth and milk. Simmer until thick and silky, 3–5 minutes.
Off heat, stir in Dijon, Worcestershire, lemon juice, and pepper. Fold in sour cream.
Stir in Gruyère and cheddar, reserving a small handful for topping.
Blanch broccoli in salted boiling water 2 minutes. Drain well and pat dry.
Combine broccoli with onion-cheese sauce. Spread mixture in the prepared dish.
Top with reserved cheese. Toss panko and fried onions with 1 tbsp oil and a pinch salt.
Scatter topping evenly over casserole. Bake 20–25 minutes until bubbling and golden.
Broil 1–2 minutes for extra color, watching closely. Rest 10 minutes before serving.
Notes
Swap half the Gruyère for Swiss or provolone, or stir in a pinch of smoked paprika. For make-ahead, assemble without the topping, cover, and refrigerate up to 24 hours; add topping and bake, adding 5–10 minutes to cook time. Serve with a crisp salad or roasted chicken.This recipe is an original creation inspired by classic French Onion Broccoli Cheese Casserole flavors. All ingredient ratios and instructions are independently developed.