Heat a skillet on the stove over medium heat, and add in the oil. Once hot, add the sliced onions. Cook them gently, stirring often, until they begin to caramelize, about 10-15 minutes.
Add in the minced garlic, and cook until fragrant, about 30 seconds to a minute.
Push the onions to the side of the pan, then add the butter to the empty side. Once it's fully melted, add in the flour and mix well, until it makes a bubbling golden paste.
Slowly pour the chicken broth into the butter and flour mixture, only a few drops at a time! Mix thoroughly the entire time. Then mix in the onions and garlic.
Bring the gravy to a boil, then reduce to medium low heat. Let simmer until thickened to your desired consistency, about 15 minutes, while giving it a whisk every few minutes. Then serve, and enjoy!
Notes
Make sure to caramelize the onions very slowly! You can caramelize them as much as you'd like, depending on how much time you have. True caramelized onions take upwards of half an hour to cook!
Make sure not to burn the onions by cooking on a higher temperature. The burned flavor can permeate the entire gravy.
You'll want nice large yellow onions. If your onions are smaller, use more! I recommend about one and a half medium onions to stand in for one large onion.
Make sure to taste test the gravy to see if it needs more salt or any other flavor.