Using a food processor, pulse the peaches until they are pea-sized chunks. Alternatively, dice the peaches by hand and in a large bowl, lightly mash them to release juices. Cover with a towel and set aside.

In a large mixing bowl, whisk together the sweetened condensed milk, heavy whipping cream, and vanilla paste on a medium-high speed until stiff peaks form.

Gently fold in the peaches until just combined.

Pour the mixture into a bread pan or other freezer safe container, and freeze at least 4 hours for soft-serve style or 6 hours and up to overnight.