Combine shallots and oil in a small saucepan over medium heat. Cook, stirring constantly, 15 to 20 minutes, until shallots are golden brown and crisp. Don't increase the heat--the sugars in the shallots will caramelize too quickly and burn.
Transfer shallots to paper towels to drain, spreading slices in a single layer. Strain oil and save to fry more shallots if you like; it keeps, chilled airtight, several weeks.
Note: Nutritional analysis is per tbsp.
* Percent Daily Values are based on a 2,000 calorie diet. Your daily value may be higher or lower depending on your calorie needs.