An entity can't be a subsidiary and a branch at the same time ...
A foreign-owned single-member LLC that doesn't elect to︀ be taxed as a corporation is a disregarded entity, it doesn't matter if it's owned︁ by a physical or legal person.
If an LLC is considered non-ETBUS, it's not taxed︂ in the US at all, period, because it doesn't derive it's profit from the US.︃ It's place of business, it's permanent establishment, and place of effective management are elsewhere. It︄ only has a registered address in the US, that's all. It is most likely taxable︅ in the place where you actually do the work, or do the management.
The Polish︆ IP box is a good idea. Also good idea is a Romanian micro-company. Revenue tax︇ is only 3% or 1% if you hire someone (min wage in Romania is 466︈ EUR). Social charges and healthcare are absolutely minimal and capped. As a single person, an︉ US LLC is in fact not a good idea, because if you run it from︊ some other country it'll be considered there as a branch of the LLC, taxed with︋ a full CIT, losing rights to any preferential treatment as a domestic company would, like︌ in case of Romania the LLC wouldn't be eligible for the 3% / 1% tax︍ rate, it'd pay the full 16%.
In the worst case it'd be recognized as tax-transparent︎ and you'd have it all taxed as your personal income.
With a Romanian company you️ can take advantage of the relaxation of CFC rules within the EU. If you create an economic substance in Romania for the company (rent office, hire someone ...), you can live anywhere in the EU and the local tax authorities can't appropriate it for taxation, it will remain Romanian with the 3% / 1% tax rate.
Moreover if you need to provide somewhere a company registration record from a public register, or board meeting minutes, anything that a normal limited company has, for example for opening a branch office, with an US LLC you cannot, because none of this exists.
You cannot hide with it︀ anymore because foreign ownership is being reported to the IRS, and the IRS passes it︁ on to your local tax authorities, along with the LLCs financial information for taxation.
I own an US LLC and after learning about all these legal rules, it seems a︂ bit pointless to have, even disadvantageous sometimes.