Holland between 2008-2018 almost always found a solid NHL player after the 1st round. It's true that some of these didn't really make the NHL until 3 or 4 years after their draft year.
2008: Nyquist, 4th round, 760 NHL games, 471 points
2009: Tatar, 2nd round, 835 NHL games, 475 points
2009: Nick Jensen, 5th round, 539 NHL games
2010: Calle Jarnkrok, 2nd round, 693 NHL games, 299 points
2010: Petr Mrazek, 5th round, 374 NHL games in net
2011: Xavier Ouelett, 2nd round, 178 NHL games
2011: Alexey Marchenko, 7th round, 121 NHL games
2012: Andreas Athanasiou, 4th round, 470 NHL games
2013: Tyler Bertuzzi, 2nd round, 381 NHL games and counting
2013: Mattias Janmark-Nylen, 3rd round, 529 NHL games
2014: None (4th rounder Christopher Ehn didn't really do enough for me to count)
2015: None
2016: Filip Hronek, 2nd round, 368 NHL games, 199 points and counting
2017: Gustav Lindstrom, 2nd round, 151 NHL games (I'd consider him a borderline "NHLer")
2018: None, or Berggren a borderline NHLer with 76 NHL games but still some time