Discussion
Solution

Summary below:
In your functionList.xml in the N++ install directory, in the “<associationMap>” section at the top, add:

<association id="markdown" userDefinedLangName="Markdown"/>
<association id="markdown" ext=".md"/>

And then at the bottom, in the <parsers> section, add:

    <!-- ==================================================== [ Markdown ] -->

    <parser
    displayName="Markdown"
    id   ="markdown"
    commentExpr="(?x)             # free-spacing (see `RegEx - Pattern Modifiers`)
      (?ms:               # Code block
        ^               # ...at start-of-line a
        (?'BLOCK'\x7E{3}(?!\x7E)|\x60{3}(?!\x60))     #  block-start indicator
        \w*\h*$             #
        .*?             # ...whatever,
        ^\x20{0,3}            # ...optional indentation for a
        \k'BLOCK'             #  block-end indicator
        \h*$            #  with trailing white-space only
      )
      "
    >
    <function
      mainExpr="(?x)            # free-spacing (see `RegEx - Pattern Modifiers`)
        (?m-s)            # ^ and $ match at line-breaks, dot does not
        ^               # at start-of-line
        (?'NOCODE_INDENT'
        \x20{0,3}(?!\x20)         # indent of 3 spaces max, otherwise it's code
        )
        (?:             # ATX-style heading
        (?'LEVEL'\x23{1,6}(?!\x23))       # nr. of hashes indicate level
        \h*             # whitespace?  ( use '+' instead of '*' for at least one white-space)
        \K            # discard text matched so far
        (?:
          [^\r\n\x5C]
        |   \x5C.           # backslash escape sequence
        )+
        (?:             # closing sequence
          \h+           # ...starts w/ at least one white-space
          \x23+           # ...contains only hashes, amount arbitrary
        )?            # ...is optional
        \h*$            # trailing white-space up till line-break
        |               # Setext-style heading
        \K            # discard text matched so far
        [^\r\n]+          # whatever,
        (?=             # ...up till
          \h*(?:\r?\n|\n?\r)        # ...any trailing white-space and a line-break,
          (?&amp;NOCODE_INDENT)       # ...indent for header indicator
          (?:={3,}|-{3,})         # ...H1- or H2-header indicator resp.,
          \h*$          # ...trailing white-space up till line-break
        )
        )
      "
    >
      <functionName>
      <nameExpr expr="(?x)
        (?|
          (?:\h+\x23+\h*$)
          [^\r\n]+
          (?=
          \h+\x23
          )
        |   .*
        )
        "
      />
      </functionName>
    </function>
    </parser>

Cheers.