Can I expense an office cottage I built in my backyard (self-employed)?

The expense to build it is all direct expense.  That portion will be depreciated.  

Other items such as insurance, heat, electricity and potentially real estate taxes and monthly fees can be deducted directly.

You can claim this as an office, provided you can meet this criterion.

Here are some details about this deduction to help you determine if you can claim it:

• Employees are not eligible to claim the home office deduction.
•  The home office deduction is available to both homeowners and renters.
• There are certain expenses taxpayers can deduct. These may include mortgage interest, insurance, utilities, repairs, maintenance, depreciation and rent.
• You must meet specific requirements to claim home expenses as a deduction. Even then, the deductible amount of these types of expenses may be limited.
• The term "home" for purposes of this deduction:
  • Includes a house, apartment, condominium, mobile home, boat or similar property.
  • Also includes structures on the property. These are places like an unattached garage, studio, barn or greenhouse.
  • Doesn't include any part of the taxpayer's property used exclusively as a hotel, motel, inn or similar business.
• Generally, there are two basic requirements for the taxpayer's home to qualify as a deduction:
  • There generally must be exclusive use of a portion of the home for conducting business on a regular basis. 
  • For example, a taxpayer who uses an extra room to run their business can take a home office deduction only for that extra room so long as it is used both regularly and exclusively in the business.
  • The home must generally be the taxpayer's principal place of business.

Please review:   How small business owners can deduct their home office from their taxes.