In the bowl of a stand mixer (or in a large, deep bowl if using a hand mixer), combine cold cream, sweetened condensed milk, salt, and vanilla.
Combine on low speed and then increase the speed to medium-high and whisk until the whisk leaves tracks in the cream and the mixture has thickened up a bit.
Combine the strawberry coulis (recipe here) and milk and add to the mixing bowl. Continue to whip until thick. Don't let the mixture reach even soft peaks, but it should softly mound and only smooth out if you shake the bowl.
Scrape the ice cream into a 9" x 5" loaf pan, press plastic wrap down on the surface, and freeze until firm, at least six hours.
Notes
For Extra Strawberry Flavor
Use 12 oz (340 grams) of strawberry puree and leave out the milk entirely for a more intense strawberry flavor and color.