Remove stems from blossoms and reserve. Remove pistils from flowers and discard. Chop stems into 1/4-inch pieces.

In a large nonstick skillet, heat extra-virgin olive oil over medium heat. Add chopped stems, shallot and generous pinch salt and pepper; cook, stirring occasionally, until tender, about 8 minutes. Remove from heat and let cool, then transfer to the bowl of a food processor. Add shrimp and marjoram; pulse until finely chopped. 

Transfer shrimp mixture to pastry bag. Snip a 1/3-inch opening and pipe filling into blossoms. Using your fingers, gently press petals around filling.

In a large bowl, whisk together flour, cornstarch and generous pinch salt. In a second clean, dry bowl, beat egg whites to soft peaks. Fold whites into flour mixture. Add sparkling water by the 1/4-cupful, stirring between additions to incorporate completely. If batter is lumpy, whisk together until smooth.

In a deep skillet, heat 1 inch oil to 360°. 

Holding petals closed and working quickly in batches, dip the blossoms, one at a time, in batter, coating blossoms completely and letting excess batter drip off. Fry coated blossoms in the oil, turning with a slotted spoon, until golden and crisp, about 2 minutes (adjust heat as necessary to keep oil around 360°). Using slotted spoon, transfer fried blossoms to paper towels to drain; sprinkle with salt. Let cool slightly before serving. Serve warm.