What your state allows
Updated
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Why it usually sits outside
Cottage food lists are built around products whose safety does not depend on a controlled process: baked goods, jams, some confectionery. A nut butter looks like it belongs on that list because it is shelf stable, and the reason it is shelf stable is not the reason those products are safe. Shelf stability and safety are different claims here more than anywhere else in this library.
Some states do allow it
A few list nut butters explicitly, sometimes with conditions attached. So "usually outside" is a starting assumption rather than a rule, and the thing not to do is infer your own position from a maker in another state or from a product you saw at a market.
Describe the product fully
What nuts, whether you roast or buy roasted, what the roast is, what else is in it, whether anything else runs through the same equipment, the jar, and where it will be sold. The roast is the detail makers leave out and it is the one that changes the answer.
Ask about the venue too
A farmers market, a retail shelf and mail order across a state line can sit differently. An answer about whether you may make it does not settle whether you may sell it where you planned to.
Record who told you what
Name, date, what you described and what they said. Guidance gets restated and staff change, and a specific conversation you can point at is a different position from a recollection.
Ask before you buy equipment
The question of where you are allowed to make this decides whether the plan works, and it is the cheapest thing on the list to ask. A roaster bought for a space that turns out not to be licensable is the expensive version of this mistake and it is entirely avoidable.