Stir 5 cups water, sugar, and rose water in large pitcher until sugar dissolves.
Add tea bags, pushing to submerge. Cover with foil; place on sunny windowsill.
Let steep until tea is dark, at least 3 hours.
Remove tea bags and discard.
Mix half and half into tea.
Pour mixture into 13x9x2-inch glass dish. Freeze until frozen around edges, about 1 hour. Coarsely chop mixture in dish. Freeze until almost solid, about 1 hour longer.
Working in 2 batches, transfer granita to processor and blend until smooth. Return to same dish and freeze 1 hour. Repeat blending in 2 batches 1 more time. Freeze 1 hour.
Using tines of fork, scrape granita in dish into flakes. Cover; freeze.
Do ahead: Can be made 1 day ahead.
Spoon granita into dishes; sprinkle with rose petals, if desired.