Place the peaches into a food processor and pulse until completely pureed.
Transfer pureed peaches to a medium saucepan and add the sugar. Cook over medium heat until mixture begins to simmer. Continue cooking and stirring for 3 minutes.
Pour mixture through a fine mesh sieve, using a rubber spatula to push as much juice from the peach solids as possible. You should end up with about 1 - 1 and 1/4 cups juice. Transfer juice to a glass measuring cup and chill in the refrigerator until cooled completely.
In the chilled bowl of a stand mixer fitted with the whisk attachment, whip the heavy cream until stiff peaks form.
Pour sweetened condensed milk into a large mixing bowl. Stir in the cooled peach juice and vanilla. Gently fold a third of the whipped cream into the condensed milk until combined. Add the rest, and continue folding until you see just a few streaks of white. Fold in most of the streusel crumble, reserving about 1/4 cup for the top.
Pour ice cream mixture into a freezer-safe container. Sprinkle reserved streusel crumble over the top.
Chill the ice cream in the freezer for at least 6 hours, preferably overnight.
Scoop, serve, and enjoy!