Combine the flour, salt, thyme, and pepper into a medium size container or bag. Cut up the beef into 1-1½" cubes and toss ½ of the beef cubes in the flour mixture. Reserve the remaining flour.
Add the olive oil to the inner pot of the Ninja Foodi and turn the sear/saute on high. When the oil is very hot, add the floured and unfloured beef cubes and brown them on all sides. This takes about 10 minutes or so.
Mince the garlic and cut one onion into large chunks and add them to the pot.
Deglaze the pot with the wine and scrape the bottom with a non-stick-safe utensil to remove the browned bits (fond) from the bottom of the pot. The wine will thicken.
Add in 2 cups of the beef broth (reserve ½ cup for later) and the Worcestershire sauce to the inner pot. Stir well. Put the pressure lid on and turn the black valve to seal. Pressure cook on high for 20 minutes. When the time is up, immediately release the pressure.
While the beef is pressure cooking, cut up the carrots into ½" slices, quarter the mushrooms, and cut the potatoes and onions into 1" pieces.
When the pressure has been released, add in the vegetables. Place the pressure lid on and turn the valve to seal. Pressure cook on high for 2 minutes. When done, immediately release the pressure.
*** follow this order exactly and use a canning jar with a metal lid, you must cool down the hot liquid BEFORE adding the flour*** Remove about 1 -1½ cups of the broth from the inner pot and place in canning jar or other container with a lid. Add remaining ½ beef broth (that is cold or room temp) and then add the flour on top. Shake well to combine the flour with the broth. Add back into the inner pot with the remaining stew and stir. Simmer on medium for 10 minutes to cook the added flour and thicken the stew.
***WHEN MIXING THE FLOUR WITH THE BROTH AT THE END, YOU MUST COOL IT DOWN WITH ROOM TEMPERATURE STOCK/BROTH BEFORE ADDING FLOUR. MIX IN GLASS ONLY, CANNING JAR WITH LID PREFERRED***I do not recommend using any flavoring packets that include thickeners as this can affect the ability for the pressure cooker to come to pressure.Everyone doesn't always like the same ingredients in their beef stew, so here are few suggestions for changing the recipe to better suit you.
Red Wine: If you don't like wine, just skip it and use all beef stock.
Mushrooms: These are totally optional, so just leave them out if you want and you don't need to make any changes.
Potatoes: If you want to cut down on the carbs a bit, consider using rutabaga chunks instead of potatoes. Rutabaga takes a little longer to cook, so I would either make your chunks ¼"-½" in size or put them in with the beef and pressure cook the entire time. I have not tested this recipe with rutabaga, so I cannot guarantee the outcome.
Tomatoes: If you like tomatoes in your beef stew, you can certainly add them in. If you usually use a thick tomato sauce, I would add that in during the 2 minute pressure cook with the veggies. Diced tomatoes can be added with the beef and pressure cooked the entire time.