This is slipskin. The curd near the rind over ripens, which prevents or greatly slows the ripening of the middle. The rind is very thick as well. And based upon what I've read here on the form, this is due to too high humidity and overly moist curds. I've had this happen to greater and lesser extents, with my second to last attempt (my first brie) a complete cheesey water bottle but my last make (a brie in a 20 cm diameter mould) turned out really well.
Some people recommend just ladelling the curds into the moulds and letting them drain. However, I would suggest cutting the curds to about 1 inch cubes (2.54 cm cubes) and stirring gently for 20 or 30 minutes to get the curds to expell some whey. The cubes should shrink up a bit. Let the curds settle a bit, then drain off most of the why. Finally, using a slotted spoon, carefully transfer the curds to the mould. This will help reduce the moisture of the curds, which in turn will help produce a firmer curd and one that is less likely to ripen too fast. Once you've got a good feel for making cams and brie, you can try direct ladelling, but I think that requires a bit of experience to know what to look for to prevent this sort of thing.
Then, make sure your curds drain really well, which will take around 24 hours, but you can let them sit longer. Flip every hour or so early on as well, but after 4 or 5 flips you can just leave them for the rest of the time. Make sure your curds are draining into a bowl and the curds are not just sitting in the liquid (i.e. put the mould up on a draining mat that is sitting on chop sticks over a bowl).
Next, make sure your cave is around 10 C, maybe as high as 12 but lower is a bit better and more controlled. The moulds work more slowly in cooler temperatures. Keep the cheeses in a box, on a draining mat, but keep an eye on the humidity. Too high and things develop too fast, resulting in, you guessed it, thick skins and running edges. As your mould grows, pat it down (i.e. just tap it with your fingers). Once you have coverage, wrap (I just use foil and it seems fine) and put them in the regular fridge (around 4 C usually) and flip each day. Again, by cooling things down things go more slowly and the outside shouldn't "cook" before the middle is done.
You've got the right things noted though, do things to reduce the moisture in the curd and keep the temperatures down. These can be a bit finicky, and I'm by no means an expert at this style of cheese, but keep at it and read lots. Others will chime in with more expert advice, and where we differ, go with them!