Cell execution does not seem to work when using async Python code

[DonJayamanne]

Originally filed by ppeetteerrs here #11525
Create a Python nb with the following cells

Cell1

from asyncio import sleep, create_task, gather
from typing import Awaitable, List
from IPython.display import display
from IPython import get_ipython

def get_msg_id() -> str:
	return get_ipython().kernel.get_parent()["header"]['msg_id']

async def say_hi_to_after(x:str, tasks: Awaitable[None]):
	current_cell_msg_id = get_msg_id()
	await tasks
	get_ipython().kernel.get_parent()["header"]["msg_id"] = x
	display("HI")
	get_ipython().kernel.get_parent()["header"]["msg_id"] = current_cell_msg_id

Cell2

x = get_msg_id()

Cell3

y = say_hi_to_after(x, sleep(2))
create_task(y);

Cell4

z = say_hi_to_after(x, sleep(3))
create_task(z);

Steps:

1. We restart the kernel and Run All (one handleExecution call with multiple cells)
2. We press Shift+Enter quickly to run all the cells consecutively (multiple handleExecution call with one cell each)

In both cases we should see HI displayed twice as the output for the second cell.