Line 2 rimmed baking sheets with double layer of paper towels. In medium bowl, stir ricotta, Pecorino, 1 egg, mint, lemon zest, salt, and pepper until smooth; set aside.
Trim blossom stems to 1 inch and remove spiny leaves at the base of flowers. Gently peel open petals and remove the pistil and any dirt inside. Briefly rinse the outsides of blossoms with water. Shake off excess water, then arrange blossoms on 1 prepared sheet. Pat blossoms dry with paper towels.
Spoon ricotta mixture into zipper-lock bag and snip off 1 corner to create ½-inch opening. Working with 1 blossom at a time, pipe enough filling into each blossom to fill green base, stopping just before orange petals begin. Gently twist petals to seal in filling, then transfer to prepared sheet. Refrigerate until ready to fry.
Add oil to large Dutch oven until it measures about 1½ inches deep and heat over medium-high heat to 350 degrees.
While oil heats, whisk flour and cornstarch together in large bowl. Whisk vodka and remaining 1 egg together in medium bowl. Whisk seltzer into egg mixture. When oil reaches 325 degrees, pour seltzer mixture into flour mixture and gently whisk until just combined (it is OK if small lumps remain).
When oil reaches 350 degrees, hold 1 blossom by stem and twirl through batter until coated. Lift blossom, allowing excess batter to drip back into bowl, then gently lower into oil. Moving quickly but carefully, repeat with 7 blossoms. Fry until crisp and lightly golden, about 2 minutes, adjusting burner, if necessary, to maintain oil temperature of 350 degrees. Using slotted spoon, transfer blossoms to second prepared sheet and season with salt to taste.
Return the oil to 350 degrees and repeat with remaining 8 blossoms. Serve immediately.
Use zucchini blossoms that measure 3 to 4½ inches in length from base to tip of blossom.
Do not omit the vodka; it is critical for a crisp coating. Using a twirling motion (like winding a watch) when dipping the blossoms in the batter encourages the petals to twist closed around the filling.
Use a Dutch oven that holds 6 quarts or more for this recipe. Be sure to begin mixing the batter when the oil reaches 325 degrees (the final temperature should be 350 degrees).