Combine 3 cups raspberries and ½ cup water in a medium saucepan. Bring to a boil over high heat. Then reduce the heat to medium and cook for 15-20 minutes, stirring occasionally. Add ½ cup water to the pot, bring to a boil for a couple of minutes, then remove from the heat.
Strain the mixture through a fine mesh sieve into a clean bowl. Use a rubber spatula to press as much pulp through the strainer as possible. Discard any solids. You should have about ¾ cup of raspberry juice at this point.
Rinse out any solids remaining in the saucepan. Then add the strained raspberry juice and 1/2 cup granulated sugar back to the pot. Bring to a boil over medium heat. Reduce the heat to low and cook for 5-10 minutes. Simmer until the syrup looks glossy and slightly thickened, but still pourable.
Remove from the heat. Stir in 1 teaspoon vanilla extract. Allow the syrup to cool to room temp, it will thicken more as it cools down.
Notes
Press the pulp gently when straining for a smoother, clearer syrup.
The syrup thickens as it cools. Simmer longer for a thicker syrup, or add a little water to thin it for drinks.
Store for 2-6 weeks in an airtight container in the back of the fridge.
Freeze cooled syrup in an airtight container or ice cube trays for easy, small portions.