Add garlic and olive oil to small saucepan, making sure the garlic is completely submerged, heating over medium-low until tiny bubbles appear.

Reduce heat to low and gently cook 15–20 minutes, stirring once or twice, until cloves are soft and golden-brown.

Remove from heat and let cool in oil.

In wide skillet, melt 3 tablespoons butter in over medium-low heat. Add onions and one teaspoon salt. Cook, stirring occasionally, until caramelized (will take around 20–25 minutes).

Stir in rosemary and cook 20–30 seconds until fragrant. Turn off heat.

Meanwhile, place potatoes in a pot, add a teaspoon of salt, and completely cover with cold water. Bring to a boil, reduce to gentle simmer, and cook until fork-tender, 15–18 minutes. Drain well.

Mash potatoes until mostly smooth. Mash in garlic confit cloves until incorporated.

Add remaining 1 tablespoon butter, 2 tablespoons garlic confit oil and ⅓ cup warm milk. Mix gently, adding more milk as needed until creamy.

Gently fold in caramelized onion mixture until combined. Season with salt and pepper to taste.