Line an 8-in. square pan with plastic wrap, letting it overhang on 2 sides. Freeze.
Coarsely mash sliced berries with 2 tbsp. sugar in a medium saucepan, using a potato masher. Bring to a simmer over high heat; then reduce heat and simmer, stirring often, until slightly jamlike, 5 to 6 minutes. Set pan in a bowl of ice and water.
Beat cream in a medium bowl with a mixer until soft peaks form. Chill.
Set out a medium saucepan and 2 medium heatproof bowls (each should fit snugly in pan without touching bottom). In first bowl, whisk egg yolks with 2 tbsp. sugar and 1 tbsp. orange flower water or 2 tsp. orange zest. Put egg whites, 6 tbsp. sugar, and the salt in second bowl.
Fill saucepan with 1 in. water and bring to a bare simmer over medium heat. Set bowl with yolks in pan and whisk until thick and ribbons form at bottom of bowl, 3 1/2 to 5 minutes; don't overcook. Set aside.
Set bowl with whites in pan. Using a clean whisk, whisk until frothy and warmed through (105° on an instant-read thermometer), 1 1/2 minutes. Remove from heat and beat with a mixer on high speed until stiff peaks form.
Stir half of strawberry mixture into yolk mixture. Fold this into whites, then fold in whipped cream. Gently fold in remaining strawberry mixture, leaving some streaks. Pour into prepared pan. Wrap airtight and freeze until firm, at least 6 hours.
Combine halved berries, remaining 2 tbsp. sugar, and 1 tsp. orange flower water or 1/2 tsp. orange zest in a bowl. Unwrap semifreddo, turning onto a cutting board, and cut into 16 squares. Set 1 or 2 in each bowl. Let stand until edges soften, 10 to 15 minutes. Spoon berries around semifreddo.
*If you're concerned about eating undercooked eggs, use pasteurized eggs in the shell, such as Safest Choice (safeeggs.com); in step 6, whites will reach only soft peaks and take 10 minutes to beat. Find orange flower water with cocktail and baking supplies.
Make ahead: Through step 7, up to 2 weeks.