Technically, you are making malted beer every time you brew.
Malting is the process where barley, or other grains are sprouted. The aleurone layer on a kernel contains enzymes that begin to break down the stored starches for the new plant. The maltster then kilns the now malted barley to halt this process.
Now 2 things happen with the malted grain.
- It is sold to breweries or homebrewers who extract sugars (malt) in a mash to make beer
- Malt extract is made
Malt extract is made the same way professional and homebrewers mash grains to make wort. The wort is then concentrated (LME) or dried (DME). Now you have concentrated malt or maltose. Maltose is a disaccharide made of 2 glucose molecules.
Malt is used in a lot of food production, including your malted milkshake. Adding malt extract back to a fermented beer would produce a sweet, probably cloying taste. Maybe good for desert. Overall, I doubt it would give you the flavor you are looking for.