Add the larger amount of strawberries (6 cups / 720g) to a blender or food processor and blend until smooth and pour into a large saucepan.
Bring to a boil for 5-10 minutes while stirring occasionally. Reduce the heat to medium-low and cook until the puree has reduced to about ⅓ of its size. This can take 20-25 minutes, depending on your stove and saucepan. You should have around ¾ cup or 240g of a reduced strawberry puree (less is fine). Let the reduction cool fully.
Blend the smaller amount of strawberries (2 cups / 240g) and pour into a small saucepan. Add the sugar and cornstarch, then whisk until there are no lumps.
Boil the mixture for 1-2 minutes while stirring frequently, then reduce to medium-low heat. Cook until the puree thickens and coats the back of a spoon. This usually takes 5-10 minutes. Cook the sauce for longer for a thicker consistency, or cook for less time for a thinner consistency. Remove the saucepan from the heat and allow it to thicken further. You can also prepare the strawberry reduction and sauce a day before and chill in the refrigerator.
Add the strawberry reduction and condensed milk to a medium bowl and mix until smooth and set aside. For a smoother ice cream, you can reblend the mixture in a blender or food processor. (Note 3 for optional food coloring)
Add the chilled whipping cream to a bowl (if using a hand mixer), or the bowl of a stand mixer with the whisk attachment. Whip until you get stiff peaks.
Add the strawberry reduction mixture to the whipped cream. Using a spatula, gently fold the mixtures together until there are no more pink or white streaks. Try to avoid overmixing as this will beat the air out of the cream.
Scoop the ice cream mixture into a 9" (23cm) loaf pan, or airtight container. If you made the strawberry sauce, dollop it throughout the ice cream and lightly swirl the mixtures together with a knife. For example, you can dollop ⅓ of the ice cream mixture into the pan, swirl through a few spoons of the strawberry sauce, then repeat with the remaining ice cream and sauce (note 4).
Cover the ice cream and freeze for 4 hours (for a soft-serve consistency) or overnight (for a firmer consistency). Usually, you can scoop the ice cream straight from the freezer. However, if your ice cream is firmer, thaw it at room temperature for 5 minutes before serving.
Store leftover ice cream in the freezer for up to 3 weeks.
