Preheat the oven to 120 degrees Celsius / 250 degrees Fahrenheit.
Peel the garlic by breaking the cloves away and placing them into a heatproof bowl. Submerge in boiling hot water for 5 minutes and drain. The skin will become loose and easy to peel away.
Place the garlic cloves into an ovenproof dish and fully submerge in olive oil. It's important the garlic is fully submerged in the olive oil so it does not burn. Bake for 2 hours or until the garlic has browned in colour and is soft to touch. There should be a slight bubble to the oil while the garlic bakes.
Remove the garlic from the oven and increase the temperature to 180 degrees Celsius / 355 degrees Fahrenheit.
Separate the garlic confit cloves from the oil and reserve the oil in a glass jar to use at another time. Using the back of a spoon, mash the garlic confit cloves until a chunky paste forms.
Place the sliced potatoes in a bowl and cover with cold water. Move the potatoes around with your hand until the water has turned murky. Drain the potatoes and repeat. This time the water should run clear. Place the potatoes onto absorbent paper and pat dry with a second piece of absorbent paper. Remove as much moisture as possible.
Layer the potatoes in a baking dish (26 x 18 x 4 cm / 10 x 7 x 1.5 inches) so they are standing upright and very snug. Set to the side.
In a saucepan on a medium heat, combine the butter and 1 tablespoon of the garlic confit olive oil and cook until melted. Add the flour and garlic to the pan and whisk to form a roux. Stir constantly for 1 – 2 minutes.
Add the milk to the roux, one cup at a time and whisk until combined and lump free. Repeat this step 2 more times until you have used up all the milk. Whisk the sauce for 5 minutes or until slightly thickened.
Take off the heat and stir through the cheese with a big pinch of salt and pepper. Season to taste.
Pour the sauce all over the potatoes and sprinkle over the remaining cheese. Bake for 45 – 50 minutes. If the top is getting to golden, cover with alfoil. Serve immediately with a sprinkling of chives.