How do I avoid my food becoming brownish/dark while cooking?
The "browning" or "coloring" of food during cooking and baking1 is a reaction of temperature and/or time. As a rule of thumb, the hotter your pan or oven, the faster the food will brown.

There are two chemical reactions (or rather chains of reactions) that play a significant role in cooking:


The Maillard reaction, which affects proteins (-> browning a steak)and 
Caramelization, which affects the carbohydrates, i.e. sugars (-> baking a cake).


Both require temperatures well over 100°C (212°F), so one of the easiest preventative measures is to add water to the food you are cooking, which should keep the food at 100°C (212°F) until all water is evaporated - for example blanching or steaming vegetables instead of stir-frying them or poaching a piece of fish or chicken breast vs. pan-frying or grilling. For "dry" preparations, just don’t heat up your pan too much - often 25% or so of the maximum power will suffice- and simply stop cooking before you see browning. You may have to finish cooking it by a low-temperature method, if it's not done at that point. 

In your sample recipe, this happens when you add the cream and simmer the asparagus for another ten minutes or until soft.



1 Browning as oxidizing (e.g. leaving a cut apple exposed to air) is not part of your question, hence ignored.