Your recipe #2 is more a cake brownie. I make one very similar to your #1 recipe.
Melt 1/2 C butter with 3 sq of bitter chocolate or 6 oz bittersweet choc.
Add 1 1/4 C sugar
Beat in 3 eggs
Add 1/2 C flour
Pour into greased 8" or 9" pan
Bake 325* for 25 min
These are very fudgie and soft.
For a change I make this brownie batter but use 3/4 C flour make layer of
16 oz cream cheese
1/2 C sugar
Beat in 1 egg
Pour 1/2 batter in 9" pan
Carefully pour cream cheese on top
Put rest of brownie batter on top
Bake 45 - 50 min.
You could put all of brownie batter on the bottom and a layer of cheese on top.