Going by this tweet from Rules Manager Eli Shiffrin, yes, you can cast the Adventure this way. The cascade goes by the creature's CMC no matter what side you end up casting (so Bituminous Blast's cascade will just pass past Beanstalk Giant and reveal the next card).
The rules for cascade changed in a recent announcement on the Banned and Restricted List.
Now cascade means, in relevant part: "You may cast that card without paying its mana cost if the resulting spell's mana value is less than this spell's mana value" (C.R. 702.85a). (Mana value was formerly known as "converted mana cost".) Now, with cascade, if you exile an adventurer card whose mana value is less than that of the spell with cascade (e.g., exile Fae of Wishes with Bloodbraid Elf's cascade), you can't choose to cast it as an Adventure unless the Adventure part's mana value is likewise less than that of the spell with cascade (so to continue the example, you can't cast Granted this way since its mana value is not less than Bloodbraid Elf's of 4). This doesn't affect the example of Order of Midnight, though, since it has the same mana value as its corresponding Adventure part, Alter Fate.
EDIT (Mar. 7, 2021): Edited to conform to the text as it actually appears in the comprehensive rules.
EDIT (Nov. 19, 2021): Edited to use updated terminology and because one rule was renumbered in the meantime.
EDIT (Jun. 12, 2021): Edited slightly.
So if I have a 3cmc cascade card can I cascade into hearts desire on Lovestruck beast?
No. With cascade, you exile cards from the top of your library until you exile a card whose mana value is less than that of the spell with cascade (C.R. 702.85a). However, exiling an adventurer card such as Lovestruck Beast this way takes into account only the card's normal characteristics (here, that includes Lovestruck Beast's mana value of 3) (C.R. 716.4). For example:
With Demonic Dread's cascade ability, if you exile a Lovestruck Beast card, you keep exiling cards (you can't cast Lovestruck Beast this way, either normally or as Heart's Desire), since Lovestruck Beast is not on the stack and its mana value of 3 is not less than Demonic Dread's, which is likewise 3 (C.R. 702.85a, 716.4).
With Bloodbraid Elf's cascade ability, if you exile a Lovestruck Beast card, you stop exiling cards (since the card's mana value is 3 and Bloodbraid Elf's is 4) (C.R. 702.85a, 716.4), and you can cast that card either as Lovestruck Beast or as Heart's Desire, since in both cases, the resulting spell's mana value (3 or 1, respectively), is less than Bloodbraid Elf's of 4 (C.R. 702.85a, 716.3).
EDIT (Nov. 19, 2021): Edited to use updated terminology and because some rules were renumbered in the meantime.
Commander: *Five Color Fun-Stuff *Grixis Artifacts *Beast Tribal
Brawl: To Be Decided At Eldraine Release!
Now cascade means, in relevant part: "You may cast that card without paying its mana cost if the resulting spell's mana value is less than this spell's mana value" (C.R. 702.85a). (Mana value was formerly known as "converted mana cost".) Now, with cascade, if you exile an adventurer card whose mana value is less than that of the spell with cascade (e.g., exile Fae of Wishes with Bloodbraid Elf's cascade), you can't choose to cast it as an Adventure unless the Adventure part's mana value is likewise less than that of the spell with cascade (so to continue the example, you can't cast Granted this way since its mana value is not less than Bloodbraid Elf's of 4). This doesn't affect the example of Order of Midnight, though, since it has the same mana value as its corresponding Adventure part, Alter Fate.
EDIT (Mar. 7, 2021): Edited to conform to the text as it actually appears in the comprehensive rules.
EDIT (Nov. 19, 2021): Edited to use updated terminology and because one rule was renumbered in the meantime.
EDIT (Jun. 12, 2021): Edited slightly.
EDIT (Nov. 19, 2021): Edited to use updated terminology and because some rules were renumbered in the meantime.