Heat a saucepan or pot on medium heat. Once hot, add the oil. Saute the onion and garlic until golden brown.
Stir in the broth, scallions, and polenta, cover with a lid. Bring to a low simmer, turn the heat down accordingly. Cook the polenta according to the directions on the package; occasionally stirring to prevent it from sticking, until it is tender and creamy.
Once tender, remove from the heat and whisk in the cheese and cover with a lid to keep warm. The texture should be soft and creamy. Taste and adjust the seasoning with salt and pepper before serving.