Prepare the turbinado sugar syrup by combining sugar and water in a small saucepan. Bring the mixture to a boil, stirring occasionally until all the sugar dissolves. Reduce the heat and simmer for 5 minutes. Remove from heat and stir in vanilla. Allow the mixture to cool down.
Add half-and-half to a shallow dish wider than the rim of the martini glass. Pour sugar into a small dish. Dip the rim of one glass in half-and-half. Shake the excess off. Dip the rim of the glass into the sugar. Shake excess and set aside to dry. Repeat the process with another glass.
In a cocktail shaker, add vodka, half-and-half, turbinado syrup, pumpkin puree, pumpkin spice, and ice. Shake vigorously. Strain into the prepared martini glasses. Garnish with a dash of pumpkin spice and serve immediately.
Store the leftover syrup in an airtight container in the refrigerator up to 2 weeks. Use the syrup to sweeten other cocktails, coffee beverages or, iced tea.