You have a very generic Requirement regarding how the extend() work.

To avoid the type errors and make it generic we can define an ObjectTemplate to satisfy the Typescript compiler so that we can assign a value to the object on the fly.

type Args = {
    property: string;
    methods: { name: string; call: string; params: number }[];
}

type ObjTemplate = {
  extend: (args: Args) => void;
  [k: string]: any
}

const obj: ObjTemplate = {
  extend: (p: Args) => {
    obj[p.property] = {};
    p.methods.forEach((m) => {
      obj[p.property][m.name] = (params: any[]) =>
        m.call + "____" + params.length;
    });
  }
};

obj.extend({
  property: "Scope1",
  methods: [
    {
      name: "functionName",
      call: "function_name",
      params: 1,
    },
  ],
});

console.log(obj["Scope1"].functionName(["firstParam"]));

Code Playground

According to typescript-interface-problem I find one answer.

export const obj = {
  extend: <T extends string, O extends string>(a: {
    property: T;
    methods: { name: O; call: string; params: number }[];
  }): {
    [Prop in typeof a as Prop["property"]]: {
      [Prop in typeof a.methods[number] as Prop["name"]]: (
        ...args: any
      ) => Promise<any>;
    };
  } => {
    const obj = {} as any;
    a.methods.forEach((method) => {
      obj[method.name] = (...args: any) => {
        return Promise.resolve("success");
      };
    });

    const newObject = {
      [a.property]: obj,
    };

    return newObject;
  },
};

const extendedObj = obj.extend({
  property: "Scope1",
  methods: [
    {
      name: "functionName",
      call: "function_name",
      params: 1,
    },
  ],
});

After that, we can get this.