What's this character that looks like 七 with a ～ in the middle? And what's its history?
The character  is recorded in the following titles:


《漢簡文字類編．甘部》
《中華字海．一部》


The paleographer 季旭昇 analyses it to be a 草書 variant of「甚」.

See the entry of 甚 from the Taiwan Ministry of Education's variants dictionary.



The earliest form of「甚」compounds「匕」(a ladle or spoon) with either「甘」or「口」:




  Note: the difference between「甘」and「口」in this context doesn't make a big
  difference, as「甘」(sweet) was originally「口」with a mark, representing a piece of food in a mouth:
  
  
  
  The meaning of sweet/good flavours is extracted from the idea of tasting the food.


The entire compound form of「甚」meant contentment, happiness, at peace, as a result of being satisfied from being fed.

Later on, decorative marks (飾筆)** were added on to the character, in the shape of「八」:



Since characters weren't standardised back then, sometimes「口」and「八」were switched around:



This last form is the direct ancestor of the modern form of「甚」.


  Note: The Shuowen Jiezi explanation of「甚」comes from the misinterpretation of 「八」and「匕」as merging into「匹」:
  
  「甚，尤安樂也。从甘，从匹耦也。」


Of course, the above doesn't explain the cursive form that appears in the question. My personal speculation is that  is a result of (1) character corruption (訛變) and (2) character simplification (簡化/省略).

(1) Corruption 


  「匕」was commonly corrupted into「七」or「」very early on, as in the
  Eastern Han stele 《曹全碑》:
  
  
  
  What looks like「合七首藥神明膏」should be interpreted
  as「合匕首藥神明膏」(miraculous knife-wound-healing medicine),
  where「匕首」means dagger. Many modern forms have retained this
  corruption, such as in the character「化」, which was originally「⿰亻匕」.
  See, for example, the modern Chinese (left) form vs. the modern
  Japanese (right) form of 「化」:
  
  


(2) Simplification


  「口」was simply omitted from the final form in rapid 草書 writing.


Of course, take all this with a grain of salt; I haven't found a detailed academic commentary on the character , and welcome any corrections to this answer by anyone who has.



**The addition of decorative marks is one of the least-known, at least among general knowledge, of Chinese character components. One of the most common characters which was formed as a result of decorative marks is the character「魚」. Compare, for example, some of the earliest forms of the character:


A detailed drawing of a fish in oracle bone script:

Still quite detailed in the middle of the bronze inscription period:

Sometimes, not so detailed and more stylised:

Stylised with addition of decorative marks around the tail:



The shape of the bottom looked very similar to and was later merged with the shape of「火」, eventually turning into「灬」and causing the tail to be detached to the rest of the body. This latter form can be considered as the direct ancestor of the modern form of「魚」:


If these marks weren't added, we might see something like this today: