In a medium skillet over medium heat, melt butter and olive oil until pan is shimmery. Add sliced onion to skillet and saute 10-12 minutes, stirring occasionally until onions are a deep golden brown. Remove from heat and set aside.
In a small saucepan, heat milk, half-and-half, flour/water mixture, garlic, thyme, and nutmeg until sauce is simmering and slightly thickened. Remove from heat and season with salt and pepper to taste.
Grease a 9-in cast iron skillet (OR a round baking pan or pie plate) Layer 1/3 of sliced potatoes in bottom of pan overlapping them slightly. Top with 1/3 caramelized onions, 1/3 cream mixture and sprinkle with 1/3 cup shredded cheese. Repeat layers two more times ending with cheese on top.
Cover pan tightly with tin foil and baked scalloped potatoes at 375F 45-50 minutes until potatoes are tender and bubbly. Remove tin foil and broil scalloped potatoes under high heat 3-5 minutes until a deep golden brown. Let potatoes stand 10 minutes before serving warm. Enjoy!