This one was actually really easy. Not because there's a dearth of wonderful female characters in my favorite shows, or because I'm any less likely to fall in love with female characters, but because my brain fixated on an answer right away and refused to consider any other option. "Really?" I asked myself. "I mean, yeah, I totally love her, but favorite?" "Yep!" my brain insisted happily, and I think if I try to argue things are gonna get ugly. Apparently, my favorite female character is Parker.
Parker is fun. Let's say that first thing. She's odd and fearless and insane and beautiful to watch in action, and her sometimes-tenuous grip on reality is endearing. But she also brings out my mama-bear instinct like no other character on television, because she's so beautifully broken. And the show is brilliant at giving us the little heartbreaking moments that tell you she knows it, without ever turning her maudlin. She's been like this her entire life and she's learned to work around it, so half the time you can't even feel bad for her about it. And like Charlie, her little oddities never feel forced or fake. I'm not gonna get into the speculation on whether or not it's Asperger's, but it certainly feels like a natural way for this particular damaged human.
In addition, I cannot remember the last time I felt like I was really watching a character develop over time, especially an adult character. Parker has been growing, building herself a family, maybe finding some new patches for her missing pieces. And the impressive thing is that she's managed to do it while she's only the focus of the show about one-fifth of the time she's on screen. And that's what makes a favorite character.