So, after getting one of the Quest Board side quests that send you to the Tower of Abjuration, I began fighting a group of undead in one of the ruined buildings (the one close to the long rest spot). There is an area that is only accessible via the Fly spell (which might be a bug in and of itself) that has two Broods of Flesh inside. I attacked one and managed to kill it, but as the battle ended, I got the alert to a battle starting with the second Brood in that room, the one tucked in the corner. When that happens, the game gets stuck in the Initiative roll.
To "fix" this, I reloaded an earlier save and made sure to Fireball both Brood in the initial fight.