In a heavy-bottomed saucepan, whisk together egg yolks and sugar until well combined.
Whisk in cream and milk until yolk mixture is fully incorporated.
Place pot over medium-low heat and cook, whisking frequently, until a custard forms on a spoon and a finger swiped across the back leaves a clean line, or until custard temperature reaches 170°F (77°C).
Remove from heat and add cheddar. Let sit 1 minute, then whisk to combine.
Use an immersion blender, or carefully transfer custard to a stand-alone blender, and blend until completely smooth, about 30 seconds.
Add salt to taste, starting with a small pinch (seasoning will depend on saltiness of cheese).
Pour custard through a fine mesh strainer into an airtight container and chill in an ice bath or refrigerator until temperature drops to 40°F (4°C), about 2 hours in ice bath, or up to overnight in refrigerator.
As base chills, it might separate slightly or form a skin. If so, wait until it's completely chilled, then blend until smooth.
Churn ice cream according to manufacturer's instructions.
Transfer to an airtight container and harden in freezer for at least 4 hours before serving atop apple pie in small scoops.
