filling fare & hand-cut steak

Hello guys,

With your help I hope to get some concrete picutre about those two phrases, "filling fare" and "hand-cut steak."
As for the former, does it refer to amount of a meal which is large enough to be full?
Or does it refer to a type of food in which something is inside or between other ingredients, like sandwich?

As for the latter, I have no idea of what it is.
Do you happen to know what it is?

A steak that is cut by hands... I can't imagine it.

Any comments will be appreciated.
Thanks~!

pb

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For your reference, here are some contexts.

Q 1: Pizza, sandwiches and salads go down well on the outdoor deck or inside the big wooden barnlike structure called the Lander Bar. A Lander institution, it not only serves filling fare (although ask for your sandwiches with the dressing on the side), it’s also the place to go for climbing and mountain-biking gossip. There’s live music many nights.
Q2 : This classic Wyoming country restaurant has been serving locals hand-cut steaks and home-roasted meats for more than half a century. The family-run establishment makes most of its sauces and salad dressings from scratch, and features a long bar as well as leather dining booths. Portions are large, and plates are simple Old West American fare.