In a frying pan, add vegetable oil or shortening at least 3 inches deep. Heat the oil over medium-high heat. You will need the oil to reach a temperature of 375°F for frying the funnel cake bites. Use a thermometer to maintain the temperature.
While the oil is heating, sift together two and one-half cups of Bisquick, two tablespoons of granulated sugar, and one-quarter teaspoon of ground nutmeg.
In a separate mixing bowl, beat two eggs until foamy using an electric mixer.
Add in one-half cup of heavy cream, one and one-half cups of milk, one teaspoon of vanilla extract, four tablespoons of melted butter, and two tablespoons of vegetable oil.
Add the dry ingredients to the wet ingredients and stir together until well combined.
Scoop a tablespoon or two of batter into the heated oil. The batter will puff up and brown on the bottom. Flip it over and brown on the other side.
Place cooked funnel cake bites on paper towels to absorb excess oil.
Sprinkle cooled funnel cake bites with cinnamon sugar and serve immediately.