The site you linked mentions these projection parameters:
Map projection: Lambert Azimuthal Equal Area, ellipsoid WGS84
Center point: 48° N, 18° E.
So you have to build a custom CRS in QGIS. As a reference, search for
lambert in the list of EPSG codes to find:
+proj=laea +lat_0=90 +lon_0=0 +x_0=0 +y_0=0 +datum=WGS84 +units=m +no_defs
Copy the string to clipboard, goto
Settings -> Custom CRS tab, paste it into the parameters field, and change the center as needed:
+proj=laea +lat_0=48 +lon_0=18 +x_0=0 +y_0=0 +datum=WGS84 +units=m +no_defs
Provide a name foor the projection (e.g.
JRC laea) and hit
Now you can drag and drop the asc file to the table of content. But beware, QGIS wrongly assings a false CRS, so rightclick on the layer ->
Set Layer CRS, and select the custom CRS you just cretaed by searching for its name.
Once done, you can assign the project CRS to the same, and add a natural Earth shapefile as a reference:
Once you found it is correct, you can use
Raster -> Projections -> Warp to reproject to any other CRS. Make sure you provide the
source SRS and
target SRS, because gdalwarp is an external command, and does not know what CRS you have assigned to the asc file inside the QGIS GUI. The asc file itself has no SRS information, like Geotoff or other formats have.