Quick answer: Your cat is bringing you prey as a gift — it's a natural social behavior where cats share food with trusted companions. It's a sign of affection, not aggression.
In the wild, mother cats bring prey to kittens to teach them hunting. Domestic cats often redirect this behavior toward their owners, whom they perceive as poor hunters in need of supplemental food. Cats with strong prey drive and outdoor access do this most frequently.
Your cat isn't trying to disturb you — it's sharing something valuable. Reacting with alarm doesn't register as 'don't do this again' to a cat. The behavior is instinctive and the motivation is entirely positive from the cat's perspective.
The most reliable prevention is keeping cats indoors or using a brightly colored collar with a bell, which reduces hunting success by alerting prey. Increasing indoor play with wand toys and electronic mice also reduces outdoor hunting by satisfying the prey drive indoors.
You can't punish or train away this instinct, but bells and more indoor play reduce it effectively. Accept what does happen as an awkward but genuine gesture of care.