New Table

Yes, in Power Query, just select the date column, right-click and select Unpivot Other Columns, rename them then get rid of the attribute column. Returns this:

 

To see this work, use the M code below:

1) In Power Query, select New Source, then Blank Query
2) On the Home ribbon, select "Advanced Editor" button
3) Remove everything you see, then paste the M code I've given you in that box.
4) Press Done

let
    Source = Table.FromRows(Json.Document(Binary.Decompress(Binary.FromText("i45WMlTSUTLRN9M3MjAyADJRUKxOtJIRWN4QJm+ib4RgGiOJWiKbANJojK7RFEm1BZp9IA0m6MabIWlA1myObpUpulXIOpEMNDLGwTaBsGNjAQ==", BinaryEncoding.Base64), Compression.Deflate)), let _t = ((type text) meta [Serialized.Text = true]) in type table [#"ead#" = _t, #"Date of 1st Call " = _t, #"Date of 2nd Call " = _t, #"Date of 3rd Call" = _t, #"Date of 4th Call" = _t, #"Date of 5th Call" = _t, #"Date of 6th Call" = _t]),
    #"Changed Type" = Table.TransformColumnTypes(Source,{{"ead#", Int64.Type}, {"Date of 1st Call ", type date}, {"Date of 2nd Call ", type date}, {"Date of 3rd Call", type date}, {"Date of 4th Call", type date}, {"Date of 5th Call", type date}, {"Date of 6th Call", type date}}),
    #"Unpivoted Other Columns" = Table.UnpivotOtherColumns(#"Changed Type", {"ead#"}, "Attribute", "Call Date"),
    #"Removed Other Columns" = Table.SelectColumns(#"Unpivoted Other Columns",{"ead#", "Call Date"})
in
    #"Removed Other Columns"