Random web find, at
https://www.victorianlondon.org/words/aesthetic.htm:
Text on the page:
REFINEMENTS OF MODERN SPEECH.
SCENE – A Drawing-room in “Passionate Brompton.”
Fair Aesthetic (suddenly, and in deepest tones, to Smith, who has just been introduced to take her in to Dinner). “ARE YOU INTENSE?”
Punch, June 14, 1879
100% CIDU for me. The rest of the site is interesting, including
https://www.victorianlondon.org/index.html and especially
https://www.victorianlondon.org/index-2012.htm
Comics I Don't Understand 
Based on the header (“Refinements of Modern Speech”) I assume it was some then-current slang that quickly fell into disuse.
The cartoon is a satire on the 19th century Aesthetic Movement, which was associated with, among others, Oscar Wilde and Walter Pater. Pater in particular argued that one must live life intensely and seek beauty. The man in the cartoon is a dull country squire who undoubtedly does not live life intensely and likely has never heard of the aesthetic movement.
I would think it means pretty much what it says. “Are you (like me) committed to the grand passions of life – art, poetry, votes for women?”
From the picture, my guess is that an honest answer would be, “I am committed to the Church of England, Tory politics, and roast beef” or perhaps just, “Harumph!”
Usual John’s explanation makes sense.
My first thought about Brompton was about the Brompton folding bicycles, which have somewhat of a cult following. But 1879 is too early for that.
Would the reference to Brompton be because it was a hotbed of the aesthetic movement, or ironic, like we might refer to the high society of Gary, Indiana?
Wikipedia: “Brompton is a village near the town of Chatham in Medway, Kent, England. Its name means “a farmstead where broom grows” — broom is a small yellow flowering shrub. Today, Brompton is a suburban village and is located between Chatham Dockyard and the town of Gillingham.”
My continuing first association to the name Brompton is the “Brompton cocktail” or “Brompton mixture”, which was dispensed in hospice-like situations as pain relief for probable terminal cases. When I worked as a pharmacy technician at the university impatient pharmacy, I was there on a couple of occasions when the head pharmacist opened the safe and took out the bottle of “Cocaine USP” to add to a bottle of Brompton he was concocting.
The Brompton in question is a London neighborhood near Kensington that was particularly associated with the aesthetic movement. It was sometimes called “passionate Brompton” because it was a popular neighborhood for successful actors. There are other, rural Bromptons in England, but they were never especially known as “passionate.”
My first thought is of the Brompton Oratory, which I’ve heard of but I cannot recall in what context. Looking it up, apparently a lot of weddings took place there.
Punch often satirized the aesthetics. Two years after this cartoon, Gilbert and Sullivan’s operetta “Patience, or Bunthorne’s Bride” appeared which was all about the aesthetic movement. The character of Bunthorne was a sort of composite of Oscar Wilde, James McNeill Whistler, and others.
You think you’re so illustrious, you call yourself intense.
from Bye Bye Love by The Cars
Ooh, good one, DrJayKay–I’ve been a big Cars fan since that first album, and that song is one of my favorites, so I’m disappointed in myself for not having thought of it when I created the post!