Combine flour, salt and a few grinds of pepper in a large ziploc bag. Add shallots, seal and toss around until shallots are coated with flour mixture.
Meanwhile, heat oil in a large saucepan until it reaches 280 degrees. It’s worth using a thermometer here if you have one. If the oil is too hot, the shallots will burn and if it is too cool they will be soggy.
Transfer shallots to a fine mesh strainer and shake off any excess flour. Place half of the shallots in the pan and fry until golden brown and crispy, 2-5 minutes. Keep your eye on them, stirring frequently. If the shallots get too dark in color, they will be bitter in flavor. Remove from oil using a slotted spoon. Place on paper towels and allow to drain.
Sprinkle shallots with coarse salt and allow them to cool slightly and crisp up. Repeat with the other half of the shallots. Shallots can be used immediately or stored at room temperature for 24 hours or in the refrigerator for 5-7 days (re-crisp in the oven briefly if necessary).