On this page of the Elden Ring game guide, you will learn what the Wondrous Elixir really is, how to get it and what is required to brew it.
The Flask of Wondrous Physick is a different type of bottle that buffs your character or restores certain statistics. To get a Flask of Wondrous Physick, you need to go to one of the dungeons in the early stages of the game, more specifically Limgrave in the Third Church of Marika, north of the tall tree on the map.
However, owning just the flask is not enough to use it. To be able to use such a flask, you first need to place Crystal Tears inside it. These ingredients are what make the Wondrous Elixir such a unique potion. Mainly because each tear has a different, specific effect. For example, they can regenerate half of your heath bar or speed up your stamina bar recovery. By combining two such tears and then ingesting the Wondrous Elixir, you will gain the two specific effects contained in the ingredients, i.e. tears.
Before you can place the ingredients into the Flask, you first need to rest at the Site of Grace, then select the Mix Flask of Wondrous Physick option. A menu will pop up and you will be able to choose the ingredients to create your own unique potion that will provide you with a variety of effects.