Two brown-haired, brown-eyed people cannot produce a blonde, blue-eyed child. Just as two blonde-haired, brown-eyed people cannot produce a brunette, brown-eyed child.
Sorry, but this is partly wrong, at least. I had dark brown hair and my husband had very dark brown hair. Two of our children had blonde hair, which is recessive to the brown. So his recessive blonde combined with my recessive blonde and the result was two blonde children.
Same with brown eyes. If both the people who have brown eyes, have a recessive blue eye, then there is a 1/4 chance of producing a blue eyed child. My parents were green and brown, which are dominant, and I was blue eyed, because each of my grandfathers with blue eyes gave my parents a recessive blue gene, then 25% chance of blue eyes. I also had a best friend growing up with dark brown hair and blue eyes, and she had two sisters with red hair, and a brother with light blonde, although her father was dark brown, and her mother reddish.
But I admit I am not sure about 2 blond haired people. Just because the genetics is much more complex than just a recessive gene being expressed. Well, except for the fact that my parents were both born with blonde hair, and it became much darker as they grew older. I was born dark brown and it stayed that way until I turned gray.
I will say gray hair makes a lot more sense on me than very dark brown. With my blue eyes and fair complexion, it seems to fit more. It always shocks me to see pictures of myself before my hair turned gray. One time I even wondered why I would have dyed my hair so dark, then I remembered that was the real colour! LOL