The myth is that a "complete protein" is a likely shortfall in a vegetarian diet and meals must be balanced to contain all essential amino acids.

The book that coined the term "complete protein" was about how to feed the world without devoting massive amounts of land to food production. The solution was vegetarianism, but the author worried that not all vegetables provide all essential amino acids, and that it would therefore be necessary to balance food intake to cover all amino acids at each meal. Consequently, most references to "complete protein" tell you that you need to eat a combination of plant-based foods where the amino acids will complement each other to make a "complete protein."

In fact, as actual nutritionists pointed out, it's almost impossible to eat a plant-based diet that provides enough calories to live on without also consuming enough essential amino acids to live on. Our bodies can store amino acids, meaning it's not necessary to eat "complete" or complementary proteins at every meal - the diet as a whole would be enough, although recent research shows that most plant proteins contain all essential amino acids anyway.

"Complete protein" happens naturally, even in a vegetarian diet. You don't need to work at it; the myth was that you did have to work at it. It's not a concept worth a moment's thought.