Cette requête d'agrégation peut faire cela :
var loved_by_mom = "Loved by mom";
db.loved.aggregate( [
{ $addFields: { fieldNameValues: { $objectToArray: "$$ROOT" } } },
{ $unwind: "$fieldNameValues" },
{ $addFields: { fldType: { $type: "$fieldNameValues.v" } } },
{ $match: { fldType: "object" } },
{ $addFields: { objs: { $objectToArray: "$fieldNameValues.v" } } },
{ $unwind: "$objs" },
{ $match: { "objs.k": loved_by_mom } },
{ $project: { fieldNameValues: 0, fldType: 0, objs: 0 } }
] )