[{"Name":"Omelet","Ingredients":["Eggs","Milk","Butter"]},{"Name":"Pancakes","Ingredients":["Eggs","Milk","Butter","Flour","Sugar","Salt"]},{"Name":"Random recipe","Ingredients":["Eggs","Milk"]}]

db.collection.aggregate([{$match:{Ingredients:{$in:["Eggs","Milk","Butter"]}}},{$addFields:{OtherIngredient:{$filter:{input:"$Ingredients",cond:{$not:{$in:["$$this",["Eggs","Milk","Butter"]]}}}}}},{$match:{"OtherIngredient":[]}},{$project:{OtherIngredient:0}}])