While not a fully vegan cafe, Asakara Good Store has clearly marked vegan options. You can expect to find choices like a vegan miso tuna melt sandwich or a full Aussie-style vegan breakfast. For those with a sweet tooth (like me!), the vegan strawberry cream sandwich is a great sweet breakfast option, featuring vegan whipped cream and fresh strawberries in soft bread.
It's located about 15-20 minute walk from Osaka Castle, so it's a good dining option if that's in your itinerary. Do keep in mind that this cafe is quite popular, so you might have to wait before getting a dine-in spot.