You may have done nothing wrong, it's common for bread dough to be very sticky after mixing. If you have your measuring right and the recipe is right time and technique will turn it from sticky to smooth.
There's 3 things that will happen:
- Absorption: flour doesn't absorb moisture instantly, most gets absorbed very quickly, but then some takes a bit more time
- Breakdown of carbohydrates: Enzymes in the flour break down carbohydrates into sugars, this process uses water
- Gluten development: glutenin and gliadin are the proteins which form gluten, when they do so they use water. This will happen naturally through enzyme action and yeast action
All these processes happen naturally, and will happen in your case if you get let it sit for awhile, known as letting it autolyse. I use this step in my bread making, and it makes a big difference in the stickiness and workability of the dough. It also reduces kneading time and effort by a large factor as some of the gluten development will happen without effort. It still may be sticky after autolysing, but that will go away as you knead it, assuming you aren't using the stretch and fold technique. Try letting it sit for 20 minutes, better yet an hour.
Your dough may still be a bit sticky after all this happens as its an enriched dough with lots of butter, sugar and egg. It may even still be tacky after kneading it, that's normal too and will probably go away after your first rise.
If it's still very wet after kneading your balance to wet and dry may have been off, in which case you should knead in small amounts of flour (a spoon at a time) until it's tacky. Don't rush it and don't add too much flour or it will go the other way and be too dry. This is why I weigh everything instead of using volume measurements in baking: small amounts matter. I even weigh water because it lets me be very consistent with the results. I would recommend you get a scale and convert to metric as it just works so much easier.