How to convert a Dataset into an indexed dataset / association-of-associations given a column header?

Given a dataset as such

If "letter" is the header that is chosen, how do I convert it into an indexed dataset / association-of-associations?

i.e. How do I define f such that f[dataset_,columnHeader_] produces the following?

Please note GroupBy is close but fails as you are unable to use Part to work with the result to extract column data. eg:

data = {<|"letter" -> "a", "foo" -> 1, "bar" -> 2|>, <|"letter" -> "b", "foo" -> 3, "bar" -> 4|>, <|"letter" -> "c", "foo" -> 5, "bar" -> 6|>};
dataDS = Dataset[data];
dataDSg= GroupBy[dataDS, Key["letter"]];
dataDSg[All, "foo"] (* <- produces an error *)

Where as data in the format of an association-of-association works fine

data2 = <|"a" -> <|"foo" -> 1, "bar" -> 2|>, "b" -> <|"foo" -> 3, "bar" -> 4|>, "c" -> <|"foo" -> 5, "bar" -> 6|>|>;
data2DS = data2 // Dataset;
data2DS [All, "foo"] (* <- returns a dataset with 1,3,5 *)

Update

Some timing comparisons

(* make dataset to test *)
colHeader = CharacterRange["a", "z"];
colHeader[[1]] = "letter";
data = RandomReal[{-1, 1}, {100000, 26}];
table = Insert[data, colHeader, 1];
dataDS = Dataset[AssociationThread[table[[1]], #] & /@ table[[2 ;;]]];

Anton Antonov answer

f[ds_Dataset, ch_] := Dataset@Association@Normal@ds[All, #[ch] -> KeyDrop[#, ch] &]
fAns = f[dataDS, "letter"]; // RepeatedTiming (* 0.934 *)

kglr answer

f0 = GroupBy[##, Association@*KeyDrop[#2]] &;
f0ans = f0[dataDS, "letter"]; // RepeatedTiming (* 1.85 *)

f1 = #[GroupBy[#2] /* Map[Association@*KeyDrop[#2]]] &;
f1ans = f1[dataDS, "letter"]; // RepeatedTiming (* 1.714 *)

Sjoerd Smit answer

groupByKey[ds_, key_String] := GroupBy[ds, Function[Slot[key]] -> KeyDrop[key], First];
groupByKeyAns = groupByKey[dataDS, "letter"]; // RepeatedTiming (* 1.2 *)

some other timings that don’t produce an answer but help to put the times above into context

GroupBy[dataDS, "letter"]; // RepeatedTiming (* 0.25 *)
Dataset[Normal[dataDS]]; // RepeatedTiming (* 0.38 *)

data = {<|"letter" -> "a", "foo" -> 1, "bar" -> 2|>, <|
    "letter" -> "b", "foo" -> 3, "bar" -> 4|>, <|"letter" -> "c", 
    "foo" -> 5, "bar" -> 6|>};
dataDS = Dataset[data];

ClearAll[f];
f[ds_Dataset, ch_] := ds[Apply[Association], #[ch] -> KeyDrop[#, ch] &];

f[dataDS, "letter"]

data = {<|"letter" -> "a", "foo" -> 1, "bar" -> 2|>, <|
    "letter" -> "b", "foo" -> 3, "bar" -> 4|>, <|"letter" -> "c", 
    "foo" -> 5, "bar" -> 6|>};
dataDS = Dataset[data];

ClearAll[f];
f[ds_Dataset, ch_] := Dataset@Association@Normal@ds[All, #[ch] -> KeyDrop[#, ch] &];

f[dataDS, "letter"]

ClearAll[f0]
f0 = GroupBy[##, Association @* KeyDrop[#2]] &;

ds = Dataset @ {<|"letter" -> "a", "foo" -> 1, "bar" -> 2|>, 
        <|"letter" -> "b", "foo" -> 3, "bar" -> 4|>, 
        <|"letter" -> "c", "foo" -> 5, "bar" -> 6|>};

Row[{ds, f0[ds, "letter"], f0[ds, "foo"], f0[ds, "bar"]}, Spacer[10]]

ClearAll[f1]
f1 = #[GroupBy[#2] /* Map[Association @* KeyDrop[#2]]] &;

Row[{ds, f1[ds, "letter"], f1[ds, "foo"], f1[ds, "bar"]}, Spacer[10]]

ClearAll[f2]
f2 = #[GroupBy @ #2, All, First @ Normal @ Keys @ KeyDrop @ ##] &;

Row[{ds, f2[ds, "letter"], f2[ds, "foo"], f2[ds, "bar"]}, Spacer[10]]

ds = Dataset @ {
    <|"letter" -> "a", "foo" -> 1, "bar" -> 2|>, 
    <|"letter" -> "b",  "foo" -> 3, "bar" -> 4|>,
    <|"letter" -> "c", "foo" -> 5, "bar" -> 6|>
};
groupByKey[ds_, key_String] := GroupBy[ds, Function[Slot[key]] -> KeyDrop[key], First];
groupByKey[ds, "letter"]