eat, feed, advance, lure, incite, food baked in dough
餤 centers on consuming or enticing with food: eating, feeding, luring, or inciting. The sense of advancing or food baked in dough are less common extensions.
餤 combines 飠 (food) with 炎 (flame), likely suggesting food cooked over fire or the enticing nature of food. The exact historical development is uncertain.
The food radical 飠 beside flames 炎 suggests food being cooked or offered as a lure. Picture someone using a baked treat to entice and feed someone, advancing their own goal.
For タン, imagine a tan-colored baked dough being used to lure someone: tan -> タン, and the food entices them forward.
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Heian-period pastry made of duck or goose eggs mixed with vegetables boiled and wrapped in mochi which is then cut into squares