Preheat oven to 400°F and arrange one of the oven racks so it’s on the topmost setting and ready to go for the roasted broccoli topping.
Remove the buds from one crown of fresh broccoli. We’re not talking whole florets here — get as close to the dark green buds as you can, leaving just the most delicate stems attached to them. Set the buds aside and chop the remaining stalk into 1/4″ slices.
Heat oil in a medium sized pot over medium heat. When oil is shiny, add onion and celery and cook, stirring occasionally, until soft and translucent, about 5 minutes. Add garlic and cook for 1 minute more, stirring occasionally.
Add sliced fresh broccoli stalks and any frozen broccoli stalks, along with the vegetable stock. The liquid should just barely cover the broccoli. If it doesn’t, add more stock (or water) until it does. Bring to a boil and cook for 10 minutes, adjusting heat so that it doesn’t boil over.
Use a wire spider (or slotted spoon) to transfer the cooked broccoli and onions from the pot to your blender, along with 3 cups of the cooking liquid from the pot. ***Save the rest of the cooking liquid in the pot in case you need to adjust the consistency of your soup in the next step.***
Blend on high until smooth. It should have the consistency of cream — if it feels too thick or chunky, add more cooking liquid 1/4 cup at a time, blending between additions, until you reach your desired consistency.
Okay, now you can pour out the remaining cooking liquid from the pot. Transfer the broccoli mixture from the blender back into the pot over low heat, and stir in the cream, farro, salt, and a few grinds of pepper and let cook for 15-20 minutes.
Make your roasted broccoli topping: Toss the reserved broccoli buds from step one on a sheet pan with a drizzle of olive oil and a sprinkle of salt and pepper. Roast on the top rack of a 400°F oven for 5-7 minutes until bright/dark green and lightly charred.
Make your bacon and shallot topping: Cook slices of bacon over medium heat in a non-stick pan until crispy. Remove from pan and let cool on a paper towel. Crumble cooled bacon into pieces.In a small bowl combine flour and salt. Toss shallot rings in the flour until lightly coated.Fry the shallots in the leftover bacon fat over medium heat until crispy and light golden brown. Remove from pan to a paper towel to cool.
Make the lemon yogurt drizzle: Mix ½ cup yogurt with lemon zest and juice. The sauce should be fairly thin — more like a heavy cream than a yogurt — so add more lemon juice if it seems too thick to drizzle. Add salt to taste.