How I cook
I will usually either look into my fridge to see what's there, and assemble a dish in my imagination based on that, or I will stroll through the produce section of the grocery store and let the vegetables tell me a story. The veggie narrative will often expand to include meat, but not always. I have been 'very nearly vegetarian', at least in the kitchen and in terms of the main audience for whom I cook, for a total of about 12 years.
I do most of my cooking using a cast iron skillet on the range, covered Corning Ware dishes in the oven, and more recently using a Le Creuset enameled cast iron dish which is nice for going back and forth between stovetop and oven:
I cook primarily for others, although I like to do R&D by myself.
And...I like to eat in restaurants with an R&D palate. I try to figure out what's in dishes and how they were prepared. In particular, what sets of flavors and textures go well together? That sense of how various foods interact is the knowledge that you will need if you want to improvise. The very same skills needed to improvise are the ones you will also need to fine-tune your cooking as it goes along...'season to taste', and so on.