If using fresh strawberries, wash and hull them. If using frozen, ensure they're thawed and drained to remove excess liquid.
In a blender, combine the strawberries, coconut milk, brown sugar, lemon juice, orange juice, and vanilla extract. Blend until the mixture is smooth. For a creamier texture, add Greek yogurt to your liking at this stage.
Give the mixture a taste. Adjust the sweetness or acidity by adding a little more sugar or lemon juice if needed.
Pour the mixture into popsicle molds. If the mixture is too runny, you can wait a few minutes for it to thicken slightly in the refrigerator before pouring.
Insert popsicle sticks when the mixture is slushy (after about an hour in the freezer) to keep them upright, or use the technique of covering the mold with plastic wrap and poking the sticks through. Freeze for at least 4 hours, ideally overnight.
Run the outside of the molds under warm water for about 10-15 seconds to make the popsicles easier to remove. If necessary, let them sit at room temperature for a few minutes.
If not serving immediately, wrap each popsicle in wax paper and place them in an airtight container or ziplock bag. Store in the freezer for up to 2 weeks for optimal taste and texture.