There is nothing like a "handbook" for ATC procedures and phraseology for use by personnel providing ATC services in EU states.
There is a civil aviation authority (CAA) in each country of the EU. EASA (EU AVIATION SAFETY AGENCY) provides its own regulations for flying in EU airspace.
The EU standards are "regulated or guided" by ICAO documents and annexes.
ICAO SARPS (Standards and Recommended Practices) for each area of ICAO responsibility are published in 19 Annexes. Each Annex deals with a particular subject area and is subject to regular amendments. The details of many of them are contained in publications in the numbered ICAO Document Series.
The ICAO Documents cover a range of matters from regulations to guidance. Some are available to the public without charge while others are only obtainable at a fee.
Description of ICAO Annexes ICAO link
Description of ICAO Annexes ICAO DOC link
Documents and Annex "examples" for ATC services and personnel:
Annex 2 – Rules of the Air
Annex 3 – Meteorological Service for International Air Navigation
Annex 10/II – Aeronautical Telecommunication, Volume II (Communication Procedures)
Annex 11 – Air Traffic Services
Annex 14 - Aerodromes
Doc 4444 – PANS-ATM - Air Traffic Management – Procedures for Air Navigation Services
Doc 7030/4 – Regional Supplementary Procedures.
ICAO Doc 4444 (air traffic management)]
**EASA (EU AVIATION SAFETY AGENCY) **
EASA Supports its Member States in implementing those ICAO standards, for example through the compliance checklists (CC) (details on EASA webpage).
The CCs show the status of implementation of ICAO Standards and Recommended Practices (SARPs) in a particular State, as well as any differences that may exist between the national/European regulations and the ICAO SARPS
EASA started with eRules project..
EASA eRules will be a comprehensive, single system for the drafting, sharing and storing of rules. It will be the single source for all aviation safety rules applicable to European airspace users. It will offer easy (online) access to all rules and regulations as well as new and innovative applications such as rulemaking process automation, stakeholder consultation, cross-referencing, and comparison with ICAO and third countries’ standards.