Thanks for the replies. My goal, and it's going to take me a few years but I'm very good with genetics, is a small cow herd that has the Gyr/Gir traits of the very long ears, speckled, huge frame like my cow, Rose... but with a more beefy carcass or at least "produce" the better carcass.
I will be studying some cattle genetics to work this out. Rose is bred to a red Angus this time and I have a couple of bred heifers (red mixed stock named Ariel and a Char/Angus cross named Millie) bred to a reg Angus bull. I have a weanling Gyr bull calf but will use my sons horned Hereford bull next crop (till the Gyr bull calf is ready to breed) on Rose, Jasmine, Ariel and Millie. All bull calves to market, heifers will be sold unless they are exceptional beef type or with Rose and Jasmine, if they have some ear and good beefy type, they stay at least till matured. The following year, I'll use my Gyr bull a couple of years to assess what I need. I don't mind horns but will dehorn the keeper heifers and eventually, will work on polled but that isn't the priority at the beginning.
I am not a big producer, I love what I love and my ideal cows will be Gyr/Brahman type look, super long ears, good milker (for a beef type) but not a "milk cow" that I have to worry about udder issues, longevity for breeding for many years, big tall framed, beefy enough, polled, flashy speckled and above all else, excellent calm temperament. The reason I say beefy enough, I still like my Gyr type but I want to be able to cross these cows to a good registered beef bull and have outstanding calves for market, yet still have the beautiful cows of my dreams in my pasture. Getting to the end product (the cows) will give my brain a workout (I am an RN and I love genetics) but that is one of the best parts. I don't have to make a living on them, it's a hobby but if I can have the cow type that I want and calves that the market wants, I couldn't ask for better.
My neighbor raises Brahmousin's (Butch Rankin) and I plan to talk with him about a heifer or two that has a little more Brahman type than he uses. He's very particular about temperament and his cattle are very nice.