Fill a large heatproof bowl or your kitchen sink about halfway with ice water.
In a medium saucepan off the heat, combine the brown sugar, skim milk powder, and milk. Blend with an immersion or stick blender, mix with a handheld mixer, or whisk until smooth. Make sure the skim milk powder is wholly dissolved and that no lumps remain (any remaining sugar granules, on the other hand, will dissolve when heated). Stir in the cream.
Clip the candy or deep-fry thermometer to the saucepan and set the pan over medium heat. Cook, stirring often with a rubber spatula and scraping the bottom of the pan to prevent sticking and burning, until the mixture reaches 110°F (45°C), 5 to 10 minutes. Remove the saucepan from the heat.
Place the egg yolks in a medium bowl. While whisking constantly, slowly pour 1/2 cup (120 milliliters) hot milk mixture into the egg yolks to temper them. Continue to whisk slowly until the mixture is an even color and consistency, then whisk the egg yolk mixture back into the remaining milk mixture.
Return the saucepan to medium heat and continue cooking the mixture, stirring often, until the mixture coats the back of a spoon and reaches 165°F (75°C), 5 to 10 minutes more.
Transfer the saucepan to the ice water in the sink and let cool for 15 to 20 minutes, stirring occasionally and making certain absolutely no ice water spills into the pan. Add the vanilla and stir to combine. Pour the ice cream base through a strainer into a resealable container and refrigerate for about 8 hours.