Melt butter in large saucepan, then add brown sugar and sprinkle with cinnamon, place peeled peach halves face down. Sauté peaches until edges are brown and they are soft enough to cut with a spoon.
Let the peaches cool completely.
Divide peaches in half. Mash half of the peaches with a fork. Place in a bowl and set aside.
Take the other half and cut into chunks. (Place in an air tight container in the fridge.)
In a medium saucepan, on medium heat, stir together cream, milk, 1/2 cup of sugar, and salt. Heat until warm, barely a bubble, and not boiling.
In a large bowl, hand whisk together egg yolks and remaining 1/2 cup of sugar. Whisk until light in color, about two minutes.
Slowly pour half of the hot mixture into the egg mixture, continually whisking.
Pour the egg and cream mixture (tempered eggs) back into saucepan with remaining cream mixture. Stir gently with a wooden spoon for 2-4 minutes, until thick enough to coat the back of the spoon. Remove from heat and stir in the lemon juice, vanilla and vanilla bean.
Pour mixture through a sieve into a large bowl. Stir in the mashed peaches, cover bowl with plastic wrap and refrigerate for 4 hours, until thoroughly chilled.
Pour chilled peach ice cream base into the ice cream maker and churn according to manufacturer's instructions. It should thicken and resemble soft serve ice cream. (about 25-30 minutes)
Once thickened fold in the remaining peach chunks and transfer ice cream to an airtight container and freeze for 5-6 hrs or overnight.