Heat a medium-size pot on medium-high heat, add olive oil and butter and allow butter to melt.
Sweat the onion and garlic over medium heat until the onion is translucent and the garlic is a light golden brown.
Add the milk. Bring the milk to a quick boil and reduce to a simmer.
Season with salt and white pepper.
Reduce heat to a minimum. Then start whisking constantly and adding the semolina in a slow, steady stream. When the semolina is totally incorporated, keep whisking for another 2 minutes. Remove from the heat.
Whisk in the Parmesan cheese. Cover the pot and let rest for 2 minutes.
Serve the polenta and garnish with some fresh grated Parmesan and extra virgin olive oil.