I'm really new to Typescript, and I just can't figure this line out. The following error is noted:

Element implicitly has an 'any' type because expression of type 'string' can't be used to index type '{}'.  No index signature with a parameter of type 'string' was found on type '{}'.

If you change the type definition of the object argument to Record<string, any> it should work.

You could also use {[key: string]: any} as both tell TS to allow access to the object keys by using an index.

Is the while loop a performance optimization?
Otherwise you could neatly solve this with a .map:

export const objectEntries: typeof Object.entries = <T>(object: {
  [key: string]: T;
}) => Object.keys(object).map(key => [key, object[key]] as [string, T]);

I ended up going with @buschtoens solution, seemed tighter to me.