Make the simple syrup: Combine 1/2 cup sugar and 1/2 cup water in a small pot. Warm over low heat, stirring until the sugar dissolves. Let it cool completely.
Store any extra in the fridge for up to 2 weeks.
Muddle the raspberries: Add 1/2 cup fresh raspberries to a cocktail shaker. Gently muddle until they release their juices. You want a pulpy puree, not a paste.
Add the lemon and vodka: Pour in 1–1.5 ounces fresh lemon juice and 2 ounces vodka.
Add 1 ounce simple syrup to start.
Ice and shake: Fill the shaker with ice. Shake hard for 10–12 seconds to chill and dilute slightly.
Strain and pour: Double strain (through the shaker’s strainer and a fine mesh strainer) into an ice-filled highball or rocks glass to catch seeds and pulp.
Top and taste: If you like it lighter, add 1–2 ounces cold water or soda water. Taste and add a splash more syrup or lemon to balance as needed.
Garnish: Add a lemon wheel, a few raspberries, and a sprig of mint.
Serve immediately.