Cut off the stem end of the onions and place the cut end on the cutting board, root end up. Slice the onion in half then remove the outer dry layers.  Do not cut the root end off yet as it serves to hold the onion together while you slice it.  

Working with one onion-half at a time, lay the cut side down.  Begin cutting strips with the tip of the knife positioned just in front of the root end and slice to the cut stem end.  Make 1/4-thick slices to the entire half onion. 

Now it is time to cut off the root end.  Cut an inverted V at the root end that is attached to the slices.  This will release the onion slices.  Repeat with all the onion haves.

In a Dutch oven or a heavy-bottomed soup pot set over medium heat, add the oil and when it is hot tip the sliced onion in and toss to coat with oil. 

When the onions begin to sizzle, reduce the heat to medium-low and cook without stirring for 5-10 minutes until the edges begin to turn golden.

Continue to cook the onions for another 20-25 minutes, stirring every 5-8 minutes.  Do not stir continually as it will prevent the onions from browning.  Adjust the heat to low if you see burn spots. Be patient, and keep the heat low the entire process is going to take 50-60 minutes. 

Add 1/4 cup of the wine to deglaze the pan, cook and stir, scraping up the fond stuck to the bottom, until the wine evaporates and the onions begin to brown and stick to the bottom.  Add another splash of wine when the fond builds up and continue to stir until the wine evaporates.  

Stir in the thyme and the garlic and continue to cook, stirring often until the onions are soft and a deep caramel color.   For softer onions add additional wine and cook another 5 minutes to your desired consistency.

Season with salt and pepper and transfer to a serving dish.