In a medium saucepan, whisk together the ube halaya, whole milk, 1 cup of the heavy cream, sugar, and salt. Cook over medium heat, whisking constantly, until the mixture is smooth and just begins to steam around the edges, about 5-7 minutes. Do not boil - you're just warming it enough to dissolve the sugar and loosen the ube jam.

Pour the warm ube mixture through a fine-mesh sieve into a large bowl, pressing through with a rubber spatula to remove any fibrous bits. Let cool to room temperature, then refrigerate until completely cold, at least 2 hours or overnight. This prevents ice crystals from forming later.

In a separate large bowl, beat the remaining 1 cup heavy cream with an electric mixer on medium-high speed until stiff peaks form, about 3-4 minutes. The cream should hold its shape when you lift the beaters - be careful not to overwhip or it will turn grainy.

Add the sweetened condensed milk, vanilla extract, and ube extract (if using) to the cold ube base. Whisk until fully combined. The mixture will be a vivid lavender-purple.

Gently fold about one-third of the whipped cream into the ube mixture to lighten it. Then add the remaining whipped cream and fold with a rubber spatula, cutting through the center and turning the bowl, until no white streaks remain. Work gently to keep the mixture airy.

Transfer to a 9x5 inch loaf pan or freezer-safe container, smoothing the top. Press a piece of plastic wrap directly onto the surface to prevent ice crystals. Freeze until firm, at least 6 hours or overnight. For the creamiest texture, let sit at room temperature for 5-10 minutes before scooping.