Using a sharp knife or mandoline, slice shallots into thin rings (along the "equator") . place rings in a small bowl.
Separate shallots into rings using your fingers and toss with flour.
Fill a small pot or saute pan with about 1/2 inch of oil bring to 350 degrees Fahrenheit over medium heat.
Add shallots into the oil and fry.
The oil should drop in temperature after adding the shallots. You want to maintain the temperature around 300 Fahrenheit. Use thermometer to check temperature and adjust heat if necessary while cooking.
Once shallots are golden and the bubbling of the oil has mostly subsided, remove the shallots using a slotted spoon or perforated spatula. Be aware that the shallots will continue to get a shade darker even after they are removed from hot oil. If the shallots get a little too dark, it is OK as long as they are not totally burnt.
Place onto a plate lined with paper towels and season with salt.