Working from Italy

At the start of COVID my wife and I accelerated our plans and moved UK to Italy. She’s a citizen, and moving pre-Brexit means I could get residency and rights to cover the short period before I’m eligible for the same.

I’m employed in the UK and had my tax-code set to NT, figuring while we worked out the details I could just settle with the tax office here, and claim any double-taxation/refund from HMRC. My work is happy with me staying here, but is keen to normalise things. They’ve found the cost of outsourcing an Italian payroll to be high because of my salary so are keen to move to a contract/freelance basis.

In the past I’d used a UK Ltd, but the impatriate tax regime here makes its it attractive to keep it local. I’d also like to be able to do some side-work in Europe which I imagine will be easier/more stable with an EU company. Does anyone have any experience a.) with the scheme and b.) doing similar in Italy?

The systems seem a little arcane. Is there anything like Freeagent or interesting Fintech for company formations?

I’m attracted a little to the Estonian route as I’d like to have both more English-language control and be able to better structure/reduce my salary and hold money in the business. It is also a decent chunk cheaper to form their than in Italy. How would I get my salary within the Italian system and do social security in that route? Setup as self employed here and invoice the Estonian company?