Using a small bowl, beat the egg. Stir in milk and baking soda.
In a separate bowl, combine flour, sugar, and cream of tartar. Work butter in with fork or pastry cutter until it's resembles a course crumbly mixture.
Stir the liquid into the dry and mix until just combined. Fold in the blueberries with just a few strokes.
Pour mixture into mold or can and cover tightly. Place in a larger pot and pour boiling water to fill 2/3 full.
Simmer for 1 1/2 hours on medium high heat. As long as there is water in the pot, there is very little danger of burning the pudding.
Remove pudding to a platter and serve with the sauce.
Instructions for sauce:
Add sugar and water to small saucepan. Simmer until sugar is dissolved, and mixture begins to thicken into syrup.
Add butter, seasonings and rose syrup and stir to combine.
Pour over blueberry pudding and serve.
Notes
Don't have rose syrup? You can use lemon juice to replace the rose syrup.