Cut the slices of bacon into ½-inch pieces.
Place the stock pot or dutch oven on the stove with medium-high heat.
Cook the bacon, letting the fat render. Continually stir the bacon pieces so that they are not scorching on the bottom of the pot. Cook for 6-8 minutes.
While the bacon is cooking, cut the vegetables.
Remove the green portion of the leeks and use only the top white part. Cut the leeks in half, lengthwise. There is often dirt and grit stuck in the layers of the leeks. Carefully rinse the leeks, separating the layers to flush out the dirt.
Cut the leek halves into ¼-inch slices.
Peel and slice the carrots into ¼-inch pieces.
Cut the celery into ¼-inch slices.
Mince the garlic.
Cut the Fresno chile into small dice. Don't touch your eyes after handling the chile.
When the bacon is almost crisp, add the carrots and celery to the pan. Reduce the heat to medium. Cook for 4 minutes.
Stir to incorporate with the bacon. There will be brown fond on the bottom of the pan.
Add the leeks to the pan, stirring to incorporate. Saute for 2 minutes.
All the vegetables will cook in the rendered bacon fat.
Add the garlic and diced Fresno chile to the pan. Stir until the garlic is fragrant.
After 2 minutes, add the anchovy paste and the tomato paste to the pan.
Stir to incorporate the 2 pastes with the ingredients in the pan. The fond will release from the bottom of the pan.
After 1 - 1½ minutes, add the chicken stock, scraping the bottom of the pan.
Add parmesan cheese rind to the pot, submerging it in the stock.
Bring the stock to a soft boil.
Add the pearled barley to the pan. Simmer for 10 - 12 minutes.
While the barley is cooking, drain and rinse two cans of cannellini beans.
Add the cannellini beans to the pot when the barley is tender.
Add 1½ teaspoon of minced rosemary, 1 tablespoon of kosher salt, and ½ teaspoon of ground black pepper to the pan.
Stir the soup and cook for 5 minutes until the beans are warm.
Garnish with grated parmesan cheese.