If I understand correctly, #1 isn't the same thing. To hawk up phlegm means to cough up mucus from the throat, in order to spit it out, hopefully into a tissue.
dude's #2 is closer, but the only verb I know for it is 'to sniff' -- "sniff it up," "sniff it back," "keep sniffing," etc. In polite circles, it's not necessary to actually use the word "snot" -- too much information. Parents of young children often just say 'Don't sniff, blow!' (and hold out a tissue); or for older ones, 'Stop sniffing and go blow your nose!'
And I'm not sure how to pair that with 'condescendingly' -- you can sniff condescendingly, or you can sniff up mucus, but not really both at once. The former is an emotional expression; the latter is a sign of a bad cold or bad manners or both.
It might also be possible to use something like 'snuffle,' or even 'snort up,' and just add adjectives like 'loudly,' 'disgustingly,' etc.