Fill a large pot 1/2 to 3/4 full of water.
Place over medium high heat and bring to a boil.
Add prepared potatoes, garlic and salt. Reduce heat to medium and simmer, partially covered, for 15 to 20 minutes, or until the potatoes and garlic are fork-tender.
Drain the potatoes and garlic.
Return to the pot.
Increase heat to heat. Cook, tossing potatoes, for 1 to 2 minutes, or until all the moisture is evaporated.
Transfer to a large bowl.
Mash potatoes with garlic with a potato masher.
In a medium saucepan, add butter, oil and milk or half-and-half.
Place saucepan over medium heat and heat, stirring, until the butter has melted.
Add butter mixture to mashed potatoes. Whip with a wooden spoon or whisk to a smooth but not soupy consistency. Mash any pieces of garlic until totally pureed.
When the liquid is absorbed, taste. Add salt and pepper, to taste.
Transfer to a serving bowl
Serve immediately, hot.