All the torn and restored cards I've seen in older books, going right back to Decremps in 1784, involve burning a card and restoring all but one missing corner, then showing a matching corner from a duplicate that fits. The idea of doing this with an extra flap to restore the corner seems to have started with Hofzinser's "Lappenkarte" or "Eck-Karte" (= flap card or corner card). It's not very clear in "Hofzinser's Card Conjuring" but is nicely explained with photos in Magic Christian's big book on Hofzinser. Other versions were described in Conradi's "Der moderne Kartenknstler" and Roterberg's "New Era Card Tricks", and also sold by magic dealers from at least the 1890s onwards.
For full restorations using two cards held together (not glued), there is the Ralph Hull routine mentioned earlier, which was in "More Eye Openers" (1933) and later in "The Testament of Ralph W. Hull" (1945). More recently there was Father Cyprian's Nostalgia Torn and Restored Card, which was based on the Hull trick.