import tkinter as tk

def log_in():
    def click_ok():
        username = usr_entry_var.get()
        password = pwd_entry_var.get()

        # This is the portion that creates a connection instance
        # that I desire to later perform actions against in the
        # form of connection.doStuff()
        # I have just set it to some text here for brevity, as this
        # portion is working fine.
        connection = 'someStuffThatAuthenticates'

        login.destroy()

    login = tk.Toplevel()

    usr_lbl = tk.Label(login, text='Username:')
    usr_lbl.grid(column=0, row=0)

    usr_entry_var = tk.StringVar()
    usr_entry = tk.Entry(login, width=40, textvariable=usr_entry_var)
    usr_entry.grid(column=1, row=0)

    pwd_lbl = tk.Label(login, text='Password:')
    pwd_lbl.grid(column=0, row=1)

    pwd_entry_var = tk.StringVar()
    pwd_entry = tk.Entry(login, width=40, textvariable=pwd_entry_var)
    pwd_entry.grid(column=1, row=1)

    ok_btn = tk.Button(login, text='OK', command=click_ok)
    ok_btn.grid(column=0, columnspan=2, row=2)

def click_run():
    connection = log_in()

    # Here is where I perform actions against the returned connection instance.
    # I am just printing it here for brevity.
    print(str(connection))

root = tk.Tk()

run_btn = tk.Button(root, text='RUN', command=click_run)
run_btn.pack()

root.mainloop()