To a large and oven safe pot or dish, add the oil and set over medium-high heat. Season the chicken with salt and pepper and chop it into bite-sized pieces, adding them to the pot as you go. Cook for 5 to 7 minutes, until browned but not cooked through. Set the peas on the counter to thaw.
Meanwhile, prepare the onions, carrots and garlic.
Remove the chicken and set aside. Add the onions, carrots and garlic to the pot and sauté for 7 to 8 minutes, until the onions are softening, lowering the heat if needed. When ready, deglaze the pot with 1/2 cup/125 mL of the broth (add the broth and use a spatula to scrape cooked bits from the bottom of the pot, this adds so much flavour!). Now, add the chicken back into the pot and sprinkle the oregano, thyme, rosemary and flour over the ingredients. Stir, cooking for 2 minutes or so, until fragrant.
Whisk in the remaining broth. Increase the heat to high and bring to a boil, then reduce the heat to medium and simmer for 25 to 30 minutes, with the lid ajar, until the carrots are fork tender. Different pots need different temperatures, so simply adjust the temperature during cooking as needed to maintain a rapid simmer.
Make the biscuits. In a large mixing bowl, whisk together the flour, baking powder, salt and sugar. Cut the cold butter into cubes, and cut the cold butter into the flour mixture with your fingers, until the butter pieces are pea-sized. Stir in the milk, just until combined. Don’t overwork the dough or the biscuits will be tough! The dough will be a little sticky but this resolves when you knead it. Turn the dough out onto a floured surface and lightly knead a few times into a shaggy dough. Pat into a square about an inch thick. Use a 2-inch round cookie cutter or glass to cut into rounds. Pop the biscuits into the fridge or freezer until it's time to add them to the stew (this ensures the fluffiest result!). Preheat the oven to 450°F/230°C.
When the stew is finished simmering, (if it is too thin, see the notes for tips to thicken) add the cream to a mug, and stir in about 3/4 cup/280 mL of the stew broth into the cream, just a few spoonfuls at a time (this will prevent the cream from curdling in the stew). Stir the tempered cream mixture and the thawed peas (frozen peas can cool the stew so the biscuits don't bake as well) into the pot.
Arrange the biscuits on top of the stew, leaving space between each, and transfer the pot to the oven. Bake for 11 to 13 minutes, until the biscuits are fluffy and firm to the touch. They will be deliciously doughy on the bottoms, like dumplings, the best of both worlds! Serve warm.