Manu 5.51. He who permits (the slaughter of an animal), he who cuts it
up, he who kills it, he who buys or sells (meat), he who cooks it, he
who serves it up, and he who eats it, (must all be considered as) the
slayers (of the animal).
There are many "killers" of an animal when someone eats it's meat. The person who slaughters the animal and the person who eats it are both equally considered as the sinner. Therefore, we can also see what is the method for atoning the sin of killing a cow.
11.108. He who has committed a minor offence by slaying a cow (or bull) shall drink during (the first) month (a decoction of)
barley-grains; having shaved all his hair, and covering himself with
the hide (of the slain cow), he must live in a cow-house.
11.109. During the two (following) months he shall eat a small (quantity of food) without any factitious salt at every fourth
meal-time, and shall bathe in the urine of cows, keeping his organs
11.110. During the day he shall follow the cows and, standing upright, inhale the dust (raised by their hoofs); at night, after serving and
worshipping them, he shall remain in the (posture, called) virasana.
Parashara Smriti's Chapter 11 has a more specific atonement measure for eating beef.
- If a Brahman has partaken of any impure food, or has swallowed virile seed, or beef, or a Chandala's food, he should perform a
However, it should be noted that austerities like Chandrayana etc. are quite cumbersome to perform.