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Meat (protein) takes a little longer to digest than, say, carbohydrates like bread and rice, so it sticks around longer and keeps you feeling fuller longer. Fat can have a similar effect.

Remove the meat, the digestion happens faster and thus you feel hungry more quickly. You can compensate by adding fats and complex carbs (whole grains), among other things.

I know what you mean. I had this problem, too, when I first went vegan but I think it was just due to the initial shock of changing a lifelong eating habit. As long as you're getting all your vitamins, minerals, and nutrients you'll be fine. The most important thing for vegans to be especially mindful of is B12, iron, and Omega 3s. I could recommend some books or YouTube channels to help you, if you like.

One of my favorites is Bite Size Vegan as she has a wealth of information there! Colleen Patrick-Goudreau is awesome, too.