What’s the best way to repair solid glass ornaments and decorations?

My dear sister and brother-in-law sent a beautiful hand-made glass palm tree ornament with fronds and its own little string of Christmas lights. Due to a miscommunication between me and my darling spouse, it went crashing to the counter within a few minutes of being opened and several of the fronds have broken off. We were both so sad. I’d like to fix it and would prefer to use a precision torch and glass rather than glue to do it right. What’s the best approach with small-scale glassmaking or jewelry repair equipment to do this?