In a medium bowl, whisk together sugar, cornstarch, and salt until no lumps remain. This prevents clumping when you add the dairy.

Pour cream and milk into a medium saucepan. Heat over medium heat, stirring occasionally, until steaming and small bubbles form around the edges - about 5 minutes. Do not boil.

Whisk 1/2 cup of the warm dairy into the sugar mixture to create a smooth slurry, then pour back into the saucepan. Cook over medium heat, stirring constantly with a wooden spoon or heatproof spatula, until the mixture thickens enough to coat the back of the spoon - about 3 to 4 minutes. You'll know it's ready when you can draw a line through the coating and it holds.

Strain the base through a fine-mesh strainer into a clean bowl to remove any cooked egg bits (even though this is eggless, straining ensures silkiness). Press plastic wrap directly onto the surface to prevent a skin, then refrigerate until completely cold - at least 4 hours, preferably overnight.

Stir in blue food coloring, vanilla, lemon, orange, and raspberry extracts. The color should be vivid sky blue - add more coloring a few drops at a time if needed. Churn in your ice cream maker according to manufacturer's instructions until thick and creamy, usually 20 to 25 minutes. It will look like soft-serve when done.

Transfer to an airtight container, press parchment paper directly on the surface, seal, and freeze until firm enough to scoop - at least 4 hours. For the best texture, let sit at room temperature for 5 minutes before serving.