Beef Medallions with Spring Mashed Potatoes

1 1/2 lb. Yukon Gold potatoes, peeled and cut into 1-inch pieces 

1 tsp. coarse kosher salt, plus more, to taste  

3 Tbs. olive oil  

1/2 head small savoy cabbage, cored and thinly sliced crosswise 

Freshly ground pepper, to taste 

2 Tbs. unsalted butter 

1 1/4 lb. beef tri-tip roast, excess fat trimmed 

2 large shallots, halved lengthwise and thinly sliced crosswise 

1 Tbs. all-purpose flour  

2 cups low-sodium beef broth 

2 Tbs. dry vermouth  

2 tsp. Dijon mustard  

1 1/2 Tbs. minced fresh thyme, plus more for garnish