Preheat oven to 400°F.
Place potatoes in a pot of salted water.
Place pot on stovetop over medium high heat. Bring to a boil and blanch potatoes for 2 minutes. Remove pot from heat and drain.
Pour olive oil into a large oven-proof sauté pan. Place over medium heat
When oil is hot and shimmering, add onions. Season with salt and pepper.
Lower heat to medium and sauté onions until caramelized, about 8 to 10 minutes.
Add garlic. Heat until fragrant, about 2 minutes more.
Turn onion mixture out into a bowl.
Place sauté pan back on stove. Add butter.
When butter has melted, cover bottom of pan with 1/3 of the potatoes.
Cover this first layer of potatoes with 1/2 of the onions.
Cover these onions with another 1/3 of the potatoes.
Cover this second layer of potatoes with 1/2 of the onions.
Finally, cover the onions with the remaining potatoes.
Place pan in the oven. Cook for 10 to 12 minutes or until the potatoes are golden brown.
Remove the pan from the oven.
Using a spatula, gently lift potatoes out of the pan.
Slice the lyonnaise into 12 slices.
Garnish with parsley.