The friendship between Mina and the Count in general.
It's implied that what solidified their friendship, despite how exasperated and annoyed the Count was by Mina's clinginess, was the fact she prevented him from being exposed to her father.
Mina's Dad: What exactly is this thing?!
Mina: He's my best friend!
The ending of the pilot. The Count is just about to hurriedly escape Mina's room since it's almost sunrise, but then he hears Mina whimper and shivering in her bed. He glides back to her, tucks her in, and kisses her forehead with a fond smile. We then see he changed his "Feeding Schedule" to a "Playtime Schedule", and all the names on the list have been replaced with Mina's.
The ending of "Playing a Hunch", when after confronted by Igor, the Count explains why he's friends with Mina despite what it would do to his reputation as an undead monster, culminating in an AnguishedPlatonic Declaration of Love.
Count Vlad: Mina's different. She's fun! She's exciting! She makes me feel alive! Igor: You're not supposed to feel alive, you're one of the undead! Vlad: …I know. I just can’t help it. I like her. (hugs Igor) I really, really, like her! (starts sobbing)
This moment from "FrankenFrog", as pictured above.
Count: (sternly) Mina… did you really reassemble this frog and resurrect him? Mina: (guiltily) …Yes… Count: (happily holds Mina up) I'm soproudof you!
At the beginning of the episode, he goes all out in fixing Mina's doll for her.
In a way, Frankenstein's monster taking the resurrected frog as his pet.
