Chocolate Mint Crock Pot Cake

Name: Chocolate Mint Crock Pot Cake
Ingredients: for the cake; 1 egg; 1/2 teaspoon teaspoon dry mustard; 3/4 teaspoon salt; 1/2 teaspoon sugar; 3 tablespoons lemon juice (from one lemon); dash of cayenne pepper; 1 cup vegetable oil, divided; 2 cups flour; 1 teaspoon baking soda; 1 1/2 cups sugar; 1/4 teaspoon salt; 6 teaspoons cocoa; 1 cup hot water; 1 teaspoon mint extract; for the peppermint cream cheese frosting; 2 sticks unsalted butter at room temperature; 8 ounces package of cream cheese at room temperature; 1 teaspoon peppermint extract; 1/2 teaspoon vanilla extract; 4- 4 1/2 cups powdered sugar; red food coloring (optional); crushed peppermint candies or starlight mints for garnish (optional)