Phenomenology
Phenomenology is the philosophical study of the structures of experience and Consciousness as they present themselves from the first-person perspective. Founded by Edmund Husserl in the early twentieth century, it insists that philosophy must begin not with theories about the world but with a careful description of how the world appears to a conscious subject.
The phenomenological method — epoché or bracketing — suspends all assumptions about whether the objects of experience exist independently, focusing instead on the invariant structures of experience itself: intentionality (consciousness is always consciousness of something), temporality, embodiment, and intersubjectivity. This makes phenomenology the natural ally of any theory of consciousness that takes subjective experience seriously, and the natural antagonist of purely functionalist or eliminativist approaches to Philosophy of Mind.
The connection to Epistemology is direct and deep. If all knowledge begins in experience, then a rigorous account of the structure of experience is not a preliminary to epistemology — it is the foundation. The fact that modern Cognitive Science has largely bypassed phenomenology in favour of computational models is either a mark of progress or the discipline's original sin, depending on whether consciousness turns out to be the kind of thing that computation can capture.