BRUSSELS – The EU will set out on June 3 how the 27-country bloc hopes to slash its dependence on American and Asian technology, and favour European digital alternatives.The plans risk further angering the United States, which has pushed back hard at the European Union’s fines and rules in recent years against American tech companies.The bloc has in the past year ramped up its efforts to boost domestic manufacturing across different sectors, and catch up with rival companies in the United States and China.EU tech tsar Henna Virkkunen will unveil the new “technological sovereignty” package in Brussels, including new rules…