Can your Monstera get big beautiful leaves?
Any Monstera Deliciosa plant has the potential to develop ever-larger leaves on any given vine. Even a tiny cutting can quickly develop large leaves with mature fenestration given the right conditions. Usually, they just keep vining out with small, heart-shaped leaves with the odd fenestration if you're lucky but it's all a matter of strategy. It helps to have a basic understanding of the monstera fenestration process.
What do you do?
The main considerations are light, nutrients, and aerial root usage. The first two seem obvious but the last one may come as a surprise. You must convince the plant that it is growing in an awesome spot, and in nature it only likes spots where there is plenty of light and its areal roots are making it to fertile soil. It is also said that cutting away the smaller leaves as it grows encourages bigger, more fenestrated leaves to grow.
The one most people ignore is the roots, often cutting them off all together. The key is to guide the roots into a medium that provides moisture and ideally nutrients. This can be accomplished by coaxing it up a thick moss pole and moistening the pole, but that's not really necessary. Unlike most Monstera species, Monstera Deliciosa doesn't really care if it climbs or not. Given good conditions it will keep putting out bigger and more beautiful leaves almost exponentially until they reach a foot or more across. So, just poke them roots back into the pot, or even into another pot, or into any place they can find water and nutrients!
How to keep the monstera mature after taking a cutting
One strategy is air layering. We'll soon have an article about this process to link, but here's a summary: Air layering refers to several strategies to propagate a plant by stimulating it to grow new roots from a branch or node before cutting it off, as opposed to taking a "cutting" then trying to get it to grow roots. When you take a cutting of Monstera Deliciosa, it is likely to lose some leaves and/or revert to a more immature form while it concentrates energy on establishing roots. By air layering, you encourage the plant to establish a viable root system before taking a cutting. Do this to the end of a vine that is already getting bigger leaves, and it will just pick up where it left off in a new pot, giving you a more compact plant with only mature leaves. This is good especially if you find the smaller scraggly stem unaesthetic. Because Monstera Deliciosa matures by aerial roots instead of growing a thicker stem, the original stem never actually grows.
A good way to accomplish air layering is to wrap a new leaf node in moss and plastic wrap or foil, near the end of a vine that is beginning to produce larger leaves. Keep the moss moist by spraying it or pouring some water in every couple days. Monstera Deliciosa tends to produce one main root per leaf, so the new leaf node will get a large root structure developed very quickly. Once the new root starts to grow and branching in the moss, cut the whole thing off and plant it, and begin fertilizing immediately and providing good light and water. It will already have a good flow of water and nutrients from the established root system, so the new leaves will not die and will continue to get bigger.