In a medium bowl, lightly beat egg yolks with ¼ cup of sugar and set aside.

In a medium saucepan, whisk together cream, milk, and remaining sugar. Whisking occasionally, heat mixture over medium-low heat until bubbles begin to form along the edges of the pan, about 8 minutes. Remove from heat and add heated cream mixture to the eggs one tablespoon at a time while whisking constantly to temper the eggs.

Once cream mixture and eggs have been combined, return to saucepan and heat on medium-low until the custard coats the back of a spoon or spatula and a line drawn with a finger leaves a distinct trail, 1 to 2 minutes. Mixture should register 170 to 175°F (77 to 79°C) on an instant-read thermometer; do not allow mixture to overheat.

Pour custard into a medium bowl and whisk in vanilla pudding mix until thoroughly incorporated. Whisk in raspberry flavoring, lemon oil, and vanilla extract until combined. Whisk in blue food coloring until desired color is reached.

Set bowl over an ice bath. Let cool at room temperature for 1 hour, stirring occasionally, then cover and refrigerate for 2 more hours or up to overnight until completely chilled. Churn chilled custard according to your ice cream maker's instructions. Transfer ice cream into a bowl or container that will hold 1 quart. Cover and freeze for at least 3 hours to fully set. Serve.