How to Make It
In a blender, puree the tomatoes with the cucumber, dill, horseradish, lemon juice and dried mushrooms and season with salt and pepper. Strain the mix through a fine-mesh sieve set over a pitcher, pressing on the solids. You should have 3 cups of Bloody Mary mix.
For each drink, fill a cocktail shaker with ice and shake 3/4 cup Bloody Mary mix with 1/4 cup of aquavit or vodka, if using. Strain into an ice-filled highball glass. Garnish with a dill sprig, cucumber slice and lemon wedge and serve immediately.