Kung Fu Hustle

In Shanghai during the 1930s, Sing and his friend Bone attempt to join the Deadly Axe Gang, which ruthlessly controls the city under the leadership of Brother Sum. Sing seeks to restore his confidence after being humiliated as a young boy while trying to protect a mute girl from bullies, due to the failure of the Buddhist Palm method he had learned from a pamphlet he bought from a beggar. Sing and Bone attempt to intimidate the residents of Pig Sty Alley but are chased off by its Landlady. Hearing of this, Sum orders the capture of Sing and Bone, while sending the Gang to reassert its authority in the wake of the humiliation. Three of the tenants, Coolie, Tailor, and Donut, reveal themselves to be martial arts masters, defeating more than fifty of the Gang. Fearing retribution, the Landlady evicts the three, but they encounter a pair of hired assassins who fight using a magical guqin that launches invisible blades. Coolie is beheaded, and Tailor and Donut are mortally wounded before the Landlady and her husband the Landlord reveal that they too are martial arts masters, having gone into self-exile after the death of their son. The two defeat the assassins but Tailor and Donut die from their injuries. The Landlords temporarily evacuate the other tenants for their safety.
Meanwhile, Sing engineers his and Bones escape from confinement, and Sum is impressed, offering them membership in the Gang if they can kill a person. Sing and Bone attempt to kill the Landlady, but their plan backfires, and Sing barely escapes from the Landlady's wrath. Seeking safety in a traffic pulpit, Sing is surprised as his body rapidly heals from the injuries sustained in the escape, the pain causing him to strike the sides of the pulpit with kung-fu-like force. Later, he attempts to mug an ice cream vendor, who turns out to be the mute girl; she offers him a lollipop but he knocks it away, humiliated at himself. After sending Bone away, blaming his failure on Bone, Sing is bought before Sum. Sum wants Sing to use his escape skills to free a legendary fighter, the Beast, from a mental asylum to use against Pig Sty Alley, offering Sing membership in the Gang for doing so. The Beast turns out to be a middle-aged, slovenly, and flippant man, but is quickly shown to be cold and ruthless.
When the Landlords arrive at the Axe Gang casino to settle the score, Sum sends the Beast to fight them. During the fight, he stabs both with hidden blades, weakening but not defeating them. Sum orders Sing to strike the Landlord to break the stalemate, but Sing has a change of heart and strikes the Beast instead. The Beast turns and pummels Sing until he is rescued by the Landlords and taken back to Pig Sty Alley. The Beast kills Sum for disrupting his fight, and then orders an all-out assault on Pig Sty Alley.
Back at the Alley, Sing undergoes a transformation brought on by the Beast's attack, fully healing himself and making him a kung-fu master himself. He sees to the well-being of the Landlords as the Gang arrives. Sing easily defeats the Gang and faces the Beast alone. The Beast uses his Toad style maneuvers to launch Sing high into the air. While aloft, Sing comes to peace with Buddha, and is able to use the Buddhist Palm method to subdue the Beast. The Beast accepts his defeat and asks Sing to be his master.
Sometime later, Sing and Bone have opened a candy store; when Sing sees the ice cream vendor outside, he invites her in to share their childhood memories. Others like the Landlords enjoy the city without fear of the Axe Gang. The same beggar that had sold the pamphlet to Sing as a child is then shown attempting to sell another one to a young boy.

Question: Who invites the ice cream vendor into the store to share their childhood memories?
Answer: Sing