One of Chipotle's (CMG) - Get Report harshest critics is done pleading its case for change in the company's board room to the slow acting executives at the burrito giant, and has opted now to go directly to a well-known activist investor for help.

In an open letter to Pershing Square's Bill Ackman -- which owns a 9.9% of Chipotle's outstanding shares -- investment firm CtW Investment Group highlighted several changes it would like to see in the company's C-Suite. First is the recruitment of at least two new, independent directors (preferably to replace existing directors, says CtW) and the separation of the CEO and chairman jobs .

The open letter to Ackman arrives a day after Chipotle announced that founder Steve Ells would assume the role of CEO and that long-time co-CEO Monty Moran would leave the company. Ells will now directly oversee restaurant operations, strategic initiatives, and innovation projects. He will continue to retain the role of chairman.

"After announcing the phase-out of Chipotle's co-CEO structure, it seems Chipotle recognizes it's time for governance reform," CtW Investment Group lead analyst Derrick Wortes says. "However, the company has already indicated it won't take all necessary steps to ensure strong, independent board oversight," Wortes adds. In November, Wortes bluntly said it was time to "clean house" with respect to Chipotle's board.

Ells continued to assert on a conference call with analysts Monday that changes to Chipotle's board were coming soon, although he hasn't detailed those changes and if that includes giving up his chairman role.

The testy relationship between CtW, which works with union-sponsored pension funds with over $250 billion in assets under management, and Chipotle dates back to 2014. It's when CtW first engaged Chipotle over the egregious compensation earned by Ells and then co-CEO Moran. It was hard to argue with their stance on the pay of Chipotle's dual CEOs.

Ells earned $13.8 million in total compensation in 2015, down from a jaw-dropping $28.9 million in 2014. Moran saw his total compensation decline to $13.6 million in 2015 from a whopping $28.1 million the year before. That despite both executives overseeing one of the biggest food safety mishaps possibly in the history of the fast-food industry, which caused diners to flee and investors to dump the stock hand over fist.

Chipotle is a mess right now

Things escalated in April of this year when CtW demanded several changes to the company's board. Citing a flawed recruitment process for board members, CtW said long-time Chipotle board members Patrick Flynn and Darlene Friedman should not be reelected at the annual meeting in May. Both are still on the board, but given that they have been targeted in the public by CtW each could be shown the door soon as part of the high level executive shake-up.

The group also cited other issues with Chipotle's board such as excessively long director tenures (a median tenure of 17 years) and low demographic diversity (all-white and overwhelmingly male).

Then in November, Amalgamated Bank and CtW filed a shareholder proposal against Chipotle to remove founder and co-CEO Steve Ells as chairman and replace him with an independent director.

Ultimately, CtW may want to consider posing a different question to Ackman -- should Ells even be the CEO? For years, Ells delegated Chipotle's operations to Moran, instead focusing on improving the ingredients of the food the company sells. So, for Ells to jump in and try and fix problems in Chipotle's increasingly complex restaurant operations, worker incentive programs, and the menu -- and also work behind the scenes to fix the board -- may be to much to handle with any form of success. Ells may be better suited for for a chairman position at Chipotle rather than a CEO tasked with running the ship day to day.

"There are pros and cons to the [management] change, as it may remove a layer of complexity and allow for more rapid changes, but it does put more on the shoulders of a management team that we believe lacks considerable depth at the top during a challenging time," points out Deutsche Bank analyst Brety Levy.

Contends Chipotle spokesman Chris Arnold, "I'd note that Steve has overseen Chipotle's restaurant operations for more of the company's history than anyone, and he has an acute sense for what makes a compelling restaurant experience."