I couldn't find a credible story of the origin of the name of this dish but I can come up with story and I am sure I will not be that far from the truth. Dawood is Arabic for David and Basha is a Turkish Ottman class title equivalent to Lord (the actual word is Pasha but we don't have "P" in Arabic). This title was given to high ranking personnel in the Ottman political system like governors and army generals. From here on the story is a no-brainer. Dawood Basaha was a nobleman somewhere in the Levant and he either liked this dish or the dish was invented in his kitchen.
Of note, there was a Dawood Pasha governor of Lebanon in the late Nineteenth century but I could not find any source to relate this dish to him.
Dawood Basha (or Daoud Pasha, as it is spelled some times) is meatballs cooked in tomato sauce and served with rice or Bulgar wheat pilaf. Chickpeas is an optional ingredients some people in Damascus like to add. The dish is a simple comfort food. The flavours are as good as the tomatoes you have so if you don't have good tomatoes you can use good quality tin tomatoes.
Similar versions of the dish are eaten across the Levant and in Egypt.
Here is my Dawood Basha recipe:
Minced lamb 500g
For large ripe tomatoes
One large onion
Tomato paste 1tbsp (adjust to taste)
Chickpeas 1 can
A slice of white bread
Chicken stock 2cups (water instead)
Start by making the meat balls. Soak the bread slice in milk and add to the meat. Add salt and allspice and mix well. Check the seasoning by frying a small amount of meat and taste. When happy, form the meat into one inch balls.
Peel your tomatoes. Cross the bottom of the tomato with a knife then drop in a boiling water for few second. The skin should come off easy. Check this video to see how. Finely chop the tomatoes or put them in a food processor.
In a heavy bottom pan heat some olive oil and fry the meat balls on all sides to brown. You don't need to cook them at this stage you just need to give them nice colour. To avoid breaking the meat balls, fry in small patches and turn around carefully. Remove the meat balls to a plate.
Thinly slice the onion and fry in the same pan on medium heat till the onions are soft. Add the tomatoes and cook for few minutes. Add the chicken stock, tomato paste, salt, pepper and some water if necessary. Cook for twenty minutes till the sauce thickens.
Add the meat balls and cook for another twenty minutes. Five minutes from the end drain and add the chickpeas.
Serve next to vermicelli rice or cooked Bulgar wheat.