I have a solution containing many different organic compounds (originally from leek and potato soup) and I would like to extract the starch from it. However, starch is insoluble in water. How could I go about extracting the starch?
You can't simply filter it and take the feed because all the vegetables fiber remain in the filter with your starch. If you want to make a starch with a decent level of purity you should start directly with the potatoes: grating the potatoes, putting them in hot water (preferably salted: this make more effective the separation from proteins) for a bit of time. Then take the filtered solution (not the residual) make the water evaporate now what you get is the starch with the potato protein, amino acids and minerals (what is called fruit water). There is this video if you want to see.
If you want to have a more pure starch also you can try to precipitate the proteins warming the solution and adding an acid. If you are at home acetic acid could be enough. Eventually you can cool down the solution this make starch precipitate so you can remove the water with a filter and take the precipitate.