No need for the drawing board. Think you just need to spend a bit of time developing your characters. Do a synopsis for each of them, and maybe one of those questionnaires. You need to be able to think like your characters and the dialogue comes so much easier then. If you imagine a conversation between yourself and someone you know well, based on a particular scenario, I'm sure you'd be able to write out the entire exchange very easily and the dialogue would be natural and realistic since you know how each of you speak, what you'd say, how you'd react etc.
A good exercise is to get to know your characters by just writing out a scene at random. One which has no real plot and you don't intend to use. Just pick a scenario where we can get an insight into their relationship (like the brothers going to buy their Father's headstone for example) and just write out their conversation. Think about how each player in the scene reacts to the others. Who is the more confident, shy, charismatic, angry, depressing, talkative, well-spoken, negative, positive, boring, interesting, funny etc. By not having to worry about the goal of the scene or a plot, you will learn a lot about your characters, and maybe even be able to use some of it in a scene later on if it's any good.
Another tip is to base you characters upon people you know, or a particular actor or famous character. Knowing them inside out, it's easier to imagine what they would realistically say in any given situation. You want your characters and their reactions to drive the story forward rather than them just being tools to tell the story. So just have in your mind what the main "conflict of the scene" is going to be about and the goal of the scene (what plot point does it convey, what has changed by the end of the scene that affects the story), and then try to let the conversational exchange in between come naturally. Rather than think, l need to mention A, B, C etc here for exposition and to set up the story, as this can often lead to the characters becoming robotic and lacking a distinct personality.