Combine the heavy cream, whole milk, granulated sugar, and vanilla extract in a large mixing bowl. Whisk until the sugar is completely dissolved and the mixture is smooth, with no granules visible.
Pour the mixture into an ice cream maker container or a freezer-safe dish. If using an ice cream maker, follow the manufacturer's instructions to churn the mixture until it reaches a soft-serve consistency, about 20-25 minutes.
If you do not have an ice cream maker, cover the dish with plastic wrap and place it in the freezer. Every 30 minutes, remove it and stir vigorously with a spatula or whisk to break up ice crystals. Repeat this process 3-4 times over 2-3 hours until the ice cream is thick and creamy.
Once the ice cream reaches a firm yet scoopable consistency, transfer it to a serving bowl or store it in an airtight container in the freezer for at least 2 hours to firm up further.
Serve the homemade vanilla ice cream with your favorite toppings or alongside fresh fruit. Observe the smooth, glossy surface and creamy texture as perfect indicators of readiness.