In a heavy-bottom saucepan, combine the milk and cream. Place over medium-low heat and cook, stirring occasionally so a skin doesn't form, until tiny bubbles start to form around the edges and the mixture reaches a temperature of 170 degrees.

Meanwhile, in a heat-proof bowl, whisk the egg yolks until smooth. Gradually whisk in the 1/3 cup sugar until the mixture is incorporated, thick, and pale yellow. This next part part is important and keeps you from having scrambled eggs in your gelato - it is called tempering the eggs. Take the mixture off of the heat. Using a ladle, scoop some of the hot milk mixture (after it gets the bubbles) and pour it into the eggs and whisk. Do this one more time, make sure to whisk well so the eggs don't have a chance to cook into scrambled eggs. Now slowly pour the egg mixture into the rest of the hot milk mixture, in the saucepan, whisking until incorporated. Return to heat and cook on low. Cook, stirring constantly with a wooden spoon until the custard is thick enough to coat the back of the spoon and/or it reaches a temperature of 185. Do not let it boil.

Pour the mixture through a fine-mesh strainer into a clean freezer-safe bowl. Let cool, stirring about every 5 minutes. Once, mixture reaches about room temperature, cover with plastic wrap - gently pressing it down until it touches the mixture to prevent a skin from forming.

Meanwhile, in a food processor, pulse peaches, cinnamon, vanilla, 1/3 cup sugar, and lemon juice until pureed. You will add the peach mixture to the custard mixture after it has cooled. You can either fill your sink with ice and place the custard bowl in an ice bath to quicken the process, or put it in the fridge and wait. Once the custard is cool, stir in the peach puree. Then refrigerate.

Refrigerate for at least four hours, but overnight is best. Pour mixture into container of ice cream machine and churn as directed. Transfer to airtight container and refrigerate for two hours before serving. Let gelato set out for 10-15 minutes before serving.