ASML is European and is arguably the most strategically important company in the entire semiconductor supply chain.
ASML is not a chip maker, it is a chip-maker maker. Still important though.
Europe should request a discount for ASML machines in a EU factory.
ASML Holding is dominating the chip technology with their machines. It's not the lack of invention or intellectual capability that holds Europe back from the digital industry, it's the lack of willing long term European invenstors. If you want to scale your digital tech startup in Europe the most viable way is to look to the US for investors.