The concrete countertops that I've seen installed were all poured somewhere else and then installed the same way granite countertops are. I'm sure its expensive but they do look nice

I did all my countertops for my outdoor kitchen and all my steps on 3 doors to the house. Quick Crete makes a counter top mix in a blue bag and its high. $25-$30. My garage was the only slick finish I had. We sprayed a release agent (Form oil) all over the garage floor and the forms(2x4's). They do sell form liners which can be used multiple times to give you a raw edge look. I did these and just tacked them up on the inside of the forms with a few finish nails.
I would suggest a small electric concrete mixer, buy one and resale it or rent one. Nothing is added to the counter top mix however we did use chicken wire in mine and it worked great. It mixes up very wet, like pour it out of a 5 gallon bucket wet. Let them set up a week before you wreck the forms. Once cured they will still try to stick to the slab on the finish side. I used all kinds of pry bars on a couple, and laying a 2x4 flat as a beater block and a sledge works pretty well. I warn you they can crack one of mine did. I would not try to do 1 solid pour around the sink. I did and mine cracked on that narrow front edge. After all this -concrete stain however you like and seal it. If all this is too much My buddy owns a concrete business and custom builds these. I sure he would do it for you. PM me and I will sen you my # if I can help